Physics Coursework: To investigate the Oscillations of a mass on a spring
Physics Coursework: To investigate the Oscillations of a mass on a spring
Aim:
In this physics coursework, I'm here to investigate the oscillations of a mass of a spring. In this investigation, the oscillation means the wave moving with periodic regularity. In this investigation, I can use any mass and many springs, so that I can investigate the oscillations.
Variables:
I believe there are many factors or variables, which can affect the time for 1 oscillation. These can be:
* Mass of weight - I believe it will have a very big impact on the time for oscillations.
* Number of springs - The number of springs will affect the affect the time for oscillations a lot just like the number of mass, because of the strength of the springs, and this depends on the number of springs. The number of springs can affect the strength of springs and this depends on the arrangement of the springs, which will be shown much more detailed below.
* Arrangement of springs - First of all, there are 2 ways to arrange the springs, and they are: Series or Parallel. Springs in series extend further than springs in parallel. Also, during the trial experiment I discovered that springs in parallel do not extend in a straight line, they move from side to side and the springs can be tangled up and this could be a major problem. Therefore, this would affect the time taken to complete the given number of oscillations. So, I will only do the springs in series, as the longer the extension, the more accurate and complex the results will be. So, the arrangement of springs will also affect the time taken to complete the given number of oscillations. It can affect the spring constant, because when the n number of springs of the same type is used in parallel, the value of spring constant is n times larger than the spring constant of one spring. When n springs of the same type are used in serial, the value of spring constant is 1/n of the spring constant of one spring.
* The efficiency of the spring - The springs keep on converting energy between the forms of elastic potential energy and kinetic energy. But the conversions cannot be 100% efficient, which means some energy is lost in the form of heat energy (by air resistance or friction) or sound. This is the main reason that the oscillation will eventually stop. However if we always choose the same type of springs, their efficiencies should be similar and the results would be much more accurate.
* The different types of springs - The different types of springs often have different spring constants, as they may be made of different materials, or the thickness of the wire of the spring may be different, or they may have different lengths etc.
* Air resistance - There is no way we can measure the air resistance, because we will need very high tech equipment for this job. Although some might think air resistance will affect only a little, still it will affect the time taken for a certain number of oscillations. However, I believe air resistance will have little effect on the wave due to the small distance it oscillates. The effect of air resistance could be unimportant, but the energy loss from potential energy to heat energy could be from the air resistance.
* The time (dependant variable) - The output variables will be the ones most affected by the mass on the spring.
* Amplitude (height) - I believe that the amplitude will affect the time of oscillations, because the mass will speed up as the height goes up, but I have not proven this yet, so I will do this first for my investigation.
* Newton's second law - If there is a resultant force, the object accelerates.
* Information given to us - Pull of load is larger than pull of spring at the start and therefore accelerates. At the middle, the pull of the load becomes equal to the pull of the spring (equilibrium), and therefore the velocity is constant, and at its fastest - Newton's first law. From the middle to the bottom, I believe the velocity will decelerate.
Hypothesis (Prediction):
I will predict that the amplitude will affect the time of 1 oscillation. If the mass starts off at much higher position than the normal position, then the time for 1 oscillation will be high. But if the mass is let go at a bit higher than the normal position of the mass, then the time for 1 oscillation will be higher. So basically, I am saying that the amplitude will affect the time of oscillations in a given time. As the amplitude goes up, the time will decrease. I think the mass will speed up more if it is let go at higher amplitude. But there is also a distance, which could also affect the time.
But I believe as the number of springs goes up and lined up in series, the time for one oscillation will take longer. Because Newton's second law states that F = M x A.
Therefore, acceleration is A = which means acceleration is inversely proportional to the mass, but in my case, I think the mass is equal to the number of springs, because they both act the same way, which is to affect the time of oscillation. We are only going to consider 2 forces for simplicity, which are gravity and the force of the spring. The only motion will be in the vertical direction, and it will not be allowed to swing or rotate. For different masses making the same oscillation, the forces are the same. Therefore, for bigger masses or longer springs, the accelerations will be smaller and thus the velocity is also smaller. It will take a longer time to complete the same oscillation.
I also believe the maximum velocity will be in the centre of the oscillation. This is because the resultant force changes direction when the mass crosses equilibrium. Just before crossing the equilibrium position, the mass is still accelerating. But just after crossing equilibrium, the resultant force is directly opposite to the velocity, therefore, it decelerates. So the maximum velocity will occur in the middle of the oscillation.
I think that the extension of the spring will be proportional to the load to a certain extent. I also believe that mass of the weight is inversely proportional to the frequency. ().
For the experiment, I am also doing on the acceleration and velocity of the graph. I think that the spring will accelerate first and in the middle, it will travel at a constant velocity and decelerate of the other end. It will do the same going up or down and will give a bell graph with time against velocity.
As you can see on the graph above, I believe, as the number of springs gets higher, the time for one oscillation will take longer. And this is a kind of graph that I expect to have in the end.
This is sort of a graph that I am expecting for the time against the velocity. The spring will accelerate quickly and then in the middle, it will travel at a constant velocity, and in the end the spring will slow down.
Variables:
I first need to decide my variables in this investigation.
Input variable: The number of springs (the strength of springs) instead of the mass. I feel the strength of the springs is much easier to do, even though the mass is similar to the strength of the springs.
Output variable: I will be doing 2 dependent variables. Time for one oscillation; in another words the period (frequency) will be my output. I will do 10 oscillations then divide it by 10 at the end to get the average of one oscillation. ...
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Variables:
I first need to decide my variables in this investigation.
Input variable: The number of springs (the strength of springs) instead of the mass. I feel the strength of the springs is much easier to do, even though the mass is similar to the strength of the springs.
Output variable: I will be doing 2 dependent variables. Time for one oscillation; in another words the period (frequency) will be my output. I will do 10 oscillations then divide it by 10 at the end to get the average of one oscillation. Also I will do the acceleration and the velocity of the load for the output variable.
Information:
In order to do this investigation, I will need to know about the oscillations deeply and clearly. Oscillation is repeated motion back and forth past a central neutral position, or position of equilibrium. A single motion from one extreme position to the other and back, passing through the neutral position twice, is called a cycle. The number of cycles per second, or hertz (Hz), is known as the frequency of the oscillation. To find out the frequency, this formula can be used:
A swinging pendulum eventually comes to rest if no further forces act upon it. The force that causes it to stop oscillating is called damping. Often the damping forces are frictional, but other damping forces, such as electrical or magnetic ones, might affect an oscillating spring.
Theory:
I have predicted that if the spring is in a vertical line, then the amplitude of the mass will affect the time of 1 oscillation, because I think the mass will speed up as the amplitude goes up. That's why the amplitude or the height will affect the time or the period of oscillations, but I will need to wait and see until I do the experiments to prove this, and see whether I am right or wrong. I also said that the extension of the spring would be proportional to the load to a certain extent. This is called the elastic limit, where the spring's strength doesn't seem to follow its graph's trend. Hooke's law is the extension, which is proportional to the load. Also the mass of the weight is inversely proportional to the frequency. () Or ().
I said in my hypothesis that the amplitude does affect the time for one oscillation, and I will try to prove that. Here are the results, which were collected.
Results table to prove that the amplitude has an affect on the time of oscillations:
Number of springs
Load (N)
Distance (cm)
Time taken to do 10 oscillations (s) 1st attempt
Time taken to do 10 oscillations (s)
2nd attempt
The average of 10 oscillations (s)
The average of 1 oscillation (s)
3
4
5
2.99
3.01
3
.3
3
4
0
3.17
3.05
3.11
.311
3
4
5
3.32
3.31
3.315
.3315
As you can see above, most of the results for the time taken to do 10 oscillations are nearly the same, even though the amplitude was different. This means that the amplitude doesn't matter when the load is let go and start oscillating. So the height won't affect the time of oscillations, so when letting the load go off the spring, it doesn't matter where you let go of it, because it won't affect the time of oscillations. So from now on, I will not measure the height (distance) anymore for each experiment. So by looking at the results, my hypothesis about the amplitude was wrong, because I said that the amplitude does affect the time of oscillation, but actually, it doesn't.
The prediction that is stated above is based on many experiments carried out previously, including the trial experiment for this investigation to find out whether the amplitude affects the time of oscillations. It is also supported by various theories and laws, which are explained below. First of all, it is common sense that the as more springs are used (series), the further down it will get pulled so the amplitude of the extension depends on the force. I have also stated the extension is proportional to the load, unless too much load is used which will go pass the elastic limit.
Firstly, this prediction is from experiments with load and its effect on the distance (length) of 1 spring when it extends. We have found out that the extension was proportional to the load 'E ? L' to a certain extent. The certain extent is called the elastic limit. The beginning of the extension up to the elastic limit is called the Hooke's Law. This is very important in this investigation.
Once the elasticity limit of the spring has been passed, it loses its functions and ignores Hooke's Law. In the beginning, the spring is very strong so the extension is very short, but as it passes the elastic limit point, the spring's extension gets longer and longer. Therefore I must be careful with this and must not put too much load onto the spring. It must be just the right and enough amount so that it won't cross the elastic limit point.
Therefore, I believe the same pattern could be followed in my investigation, because I am using springs and the mass, where the current input variable in my experiment is the number of springs.
My prediction is made relating to the velocity in different parts of the oscillation which is based on Newton's first and second laws. As I am investigating half an oscillation using a ticker-tape-timer, and I believe that at the 2 peaks, it will be at its slowest velocity and fastest at the centre of the oscillation (equilibrium). This is because firstly, starting at the top of the oscillation, pull of load is larger than pull of spring in the beginning and therefore it accelerates. In the middle, where there's equilibrium, the pull of the load becomes equal to the pull of the spring so therefore the velocity is constant, and at its fastest - Newton's first law states that if there is no resultant force, the object will remain stationery or maintain constant velocity and as you can see, the velocity is constant in this case. From the middle to the bottom, I believe the velocity will decelerate due to the air resistance and potential energy turning into heat energy from the friction where the mass is collided with the air molecules. However, I believe this will not have a very significant impact on the results. But as the time passes, the oscillation will take place very slowly gradually, but in the end, it will suddenly go stop, due to the air resistance and the potential energy turning into heat energy from the friction where the mass (load) collide with the air molecules.
The equilibrium state:
First of all by looking at the diagram, the resultant force is equal to the downward force and the mass and the spring remain unmoved due to the Newton's first law, and we call this equilibrium, where the 2 forces are equal. Now, when the spring is stretched by an external force, the weight moves down from its balanced position. There is now a displacement of the weight from its balanced position. And it is greater than the downward force (gravity) and the upward force (resultant force). Therefore, the spring and the weight accelerate upwards/downwards and the oscillation begins. The acceleration can be calculated with Newton's Second Law:
Or
But in my case, the acceleration can be defined as this: If we used a larger mass, the same forces would be seen, but lower down.
As you can see, it is now a common sense that as the number of springs gets higher, the lower the frequency (number of oscillation in a given time), and as the number of springs gets fewer, the higher the frequency.
We can also see the oscillation in terms of energy. The total amount of elastic potential energy and kinetic energy is constant; therefore there is always the transformation between the two forms of energy when the spring is oscillating. Therefore it has the basic and universal characteristics of all waves, which means the transfer of energy.
Fairness Precautions during the experiment:
There are a few things that I will need to carry out in this experiment to keep it as fair as possible to get the most accurate results. I will use the same amount of load for every experiment to be fair. As soon as the load comes up and is about to go down again, I will then start my stopwatch. I will try to use springs, which all of them have the same length to start off with. And when every experiment has finished, I will put on another spring in series. This will mean that the extension will be proportional to the load. Also, I will record the time to the nearest 2 decimal places.
st experiment apparatus List:
. 3 Springs
2. Stand and Clamp
3. 4N of Mass (Load)
4. Stopwatch
5. A ruler
Diagram of the Apparatus:
To prove that the amplitude does not affect the time of oscillations, I used this apparatus as shown below:
In this first experiment, I had to find out whether the amplitude does affect the time of oscillations or not. So, I first collected the apparatus as shown above, and then I used 3 springs + 4N of mass for each experiments, which were 3 in total. The only differences in these 3 experiments were that they all were dropped at a different height to see whether the height affected the time of oscillations or not. I did the experiment twice for each 3 experiments so that I could take the average which then the results would be far more accurate. The results all came out nearly the same, which then I concluded that the amplitude had no affect on the time taken.
By using this apparatus, I was able to see whether the amplitude affects the time of oscillations. The results for this experiment was already shown above, and the results showed very similar results even though all of them started at different heights.
Procedure:
. Set up the apparatus as shown above
2. Collect 3 springs and 4N of mass
3. Use the ruler to measure the height of the mass and pull it down to a certain distance (5cm), so that when you let go, it will start oscillating
4. Start the stopwatch as soon as letting go of the mass
5. Time how long it takes for the mass to do 10 oscillations
6. Repeat the whole procedure again with the same distance (5cm), so that the average can be taken from the 2 results
7. Repeat the whole procedure again, but with only different amplitude (10cm)
8. Repeat this procedure again with the same amplitude as the last one (10cm)
9. Repeat the whole procedure again, but with only different amplitude (15cm)
0. Repeat this procedure again with the same amplitude as the last one (15cm)
1. Compare all the results between all three different experiments
2nd experiment apparatus List:
. Springs
2. Stand and Clamp
3. Weights
4. Power supply
5. Ticker tape timer (Including carbon paper)
6. Ticker tape
7. Cello tape
Diagram of the Apparatus:
This experiment was to see whether the number of springs affected the acceleration and velocity of the oscillations.
Procedure:
To measure the difference in acceleration in an oscillation of a spring, I set up the apparatus as shown in the diagram above. Then we pulled down the springs with the weights on and attached it to the bottom of the weights and pulled it through the ticker tape timer, and then we turned on the timer and let go of the spring. We had to be careful not to let the spring start to go down again, because the tape would then have extra dots on, which could ruin our results. We did this 4 times for the spring going upwards and repeated the whole procedure for the spring going downwards by just putting the ticker tape timer on top of the stand, and attaching the tape to the top of the load.
3rd experiment apparatus List:
. Springs (Up to 7 springs)
2. Stand and Clamp
3. 4N of Mass (Load)
4. Stopwatch
Diagram of the Apparatus:
This experiment was to see whether the number of springs actually affected the time of oscillations.
In this first experiment, I had to find out whether the amplitude does affect the time of oscillations or not. So, I first collected the apparatus as shown above, and then I used 3 springs + 4N of mass for each experiments, which were 3 in total. The only differences in these 3 experiments were that they all were dropped at a different height to see whether the height affected the time of oscillations or not. I did the experiment twice for each 3 experiments so that I could take the average which then the results would be far more accurate. The results all came out nearly the same, which then I concluded that the amplitude had no affect on the time taken.
By using this apparatus, I was able to see whether the amplitude affects the time of oscillations. The results for this experiment was already shown above, and the results showed very similar results even though all of them started at different heights.
Procedure:
. Set up the apparatus as shown above
2. Collect all 7 springs and 4N of mass
3. Using only 1 spring, attach 4N of mass onto the end of the spring and pull it down a bit to start the oscillations. It doesn't matter how much you pull the mass down, because previously, I have proven that the amplitude does not affect the time of oscillations, but it is advised to pull it down just a little, so it is much easier to count the oscillations
4. Start timing as soon as letting go of the mass. Count up to 10 oscillations and stop immediately when it finishes. (I did this with my partner and we both did it twice, which sums up to 4 results which were collected for each experiment)
5. Repeat the whole procedure until 7 springs are used
6. Look at the results and analyze
Data Presentation
After the all the experiment, results would have been collected. The average of the time of 10 oscillations will be calculated. The frequency of the oscillation will be calculated from the time period. These figures will be put into the table.
Expected Results:
I will be expecting some graphs plotted from the results, which will be collected from the experiments.
I believe there is a connection between the mass and the length (number) of the springs, and the relationships between them will be something like this:
A straight line is expected when drawing the graph of load against length of spring. Normally the graph should be drawn with the length of spring against the load. The y-intercept of the regression line is expected to be less than zero, because when there is no load on the spring, the spring should still have a length.
As the number of spring increases, it is common sense that the time (period) also increases as well direct proportionally. Therefore, I expect this kind of results to be collected, where as the number of spring increases, the time (period) increases as well.
As you can see above, the frequency should be inversely proportional to the mass, and therefore, the graph should come out like this. This is a typical graph of an inversely proportional graph, where as the mass increases, the frequency gets smaller and smaller.
But if we plot this points onto number of springs against the 1 / frequency, then the graph should come out as a direct proportional straight linear line graph, just like the one above, where the straight linear line goes through the origin (0,0).
Results table to see whether the number of springs have an affect on the time of oscillations:
Number of springs
Load (N)
Distance (cm)
Time taken to do 10 oscillations (s) 1st attempt
Time taken to do 10 oscillations (s) 2nd attempt
Time taken to do 10 oscillations (s) 3rd attempt
Time taken to do 10 oscillations (s) 4th attempt
The average of 10 oscillations (s) 1st + 2nd+ 3rd+4th attempts
The average of 1 oscillation (s)
4
-
8.28
8.35
8.31
8.32
8.315
0.8315
2
4
-
0.66
0.81
0.89
0.65
0.7525
.07525
3
4
-
4.25
4.26
4.19
4.32
4.255
.4255
4
4
-
4.70
5.06
5.10
5.26
5.03
.503
5
4
-
20.44
20.53
20.31
20.48
20.44
2.044
6
4
-
8.47
8.74
8.62
8.76
8.6475
.86475
7
4
-
22.18
22.12
22.34
22.22
22.215
2.2215
The actual masses of the weights are in Newtons. However, I can change the units to kilograms by using the formula F = M x G.
For example, using the weight as 1 Newtons, we could substitute this into the formula to give:
= M x 10N/Kg
M = 0.1Kg
Graph for the results above:
On the graph above, I took the average time of 10 oscillations from 4 attempts, and this is how it looks. The trend on the graph looks just as what I had expected, because as the number of springs increases, the time it took to do 10 oscillations increases, more or less direct proportionally. This graph tells me that my hypothesis about the number of springs against the period per second was correct.
Ticker tape timer results (When moving upwards):
Number
Time (s)
Velocity (cm/s)
0.02
1.7
2
0.04
5
3
0.06
20
4
0.08
26.7
5
0.1
33.3
6
0.12
40
7
0.14
48.3
8
0.16
58.3
9
0.18
68.3
0
0.2
78.3
1
0.22
85
2
0.24
90
3
0.26
95
4
0.28
98.3
5
0.3
03.3
6
0.32
16.7
7
0.34
20
8
0.36
23.3
9
0.38
23.3
20
0.4
26.7
21
0.42
25
22
0.44
25
23
0.46
26.7
24
0.48
31.7
25
0.5
25
26
0.52
21.7
27
0.54
20
28
0.56
18.3
29
0.58
11.7
30
0.6
06.7
31
0.62
03.3
32
0.64
98.3
33
0.66
90
34
0.68
86.7
35
0.7
81.7
36
0.72
73.3
37
0.74
65
38
0.76
53.3
39
0.78
48.3
40
0.8
40
41
0.82
31.7
42
0.84
23.3
43
0.86
6.7
44
0.88
0
As you can see on the graph, the line is moving upwards, and the points (results) are very good. This is because the trend is going through most of the points, which means I can conclude that the time of oscillations has a very good relationship with the velocity of oscillations. But there are some points on the graph that which do not follow the rules like the others. This means the ticker tape timer is not 100% efficient, and only half of the graph is shown, which is not very good to us. And I will do another same experiment to see the other half of the trend. The greatest velocity on this graph can be found out. It starts at 0 and finishes at 0.9, which means the middle point is 0.45. And if we go along the y-axis, then it comes to around 125cm/s, which is the greatest speed above all the other ones.
Ticker tape timer results (When moving upwards):
Number
Time (s)
Velocity (cm/s)
0.02
-8.3
2
0.04
-13.3
3
0.06
-20
4
0.08
-30
5
0.1
-38.3
6
0.12
-46.7
7
0.14
-56.7
8
0.16
-63.3
9
0.18
-71.7
0
0.2
-81.7
1
0.22
-90
2
0.24
-101.7
3
0.26
-108.3
4
0.28
-118.3
5
0.3
-126.7
6
0.32
-133.3
7
0.34
-141.7
8
0.36
-146.7
9
0.38
-151.7
20
0.4
-156.7
21
0.42
-161.7
22
0.44
-161.7
23
0.46
-160
24
0.48
-163.3
25
0.5
-163.3
26
0.52
-161.7
27
0.54
-158.3
28
0.56
-156.7
29
0.58
-155
30
0.6
-146.7
31
0.62
-136.7
32
0.64
-126.7
33
0.66
-115
34
0.68
-103.3
35
0.7
-90
36
0.72
-78.3
37
0.74
-65
38
0.76
-53.3
39
0.78
-45
40
0.8
-35
41
0.82
-28.3
42
0.84
-21.7
43
0.86
-15
44
0.88
-10
As you can see above on the graph, this shows the other half of the graph, which is going downwards. On this graph, the greatest velocity on this graph can be found out. It starts at 0 and finishes at 0.9, which means the middle point is 0.45. And if we go along the y-axis, then it comes to around -165cm/s, which is the greatest speed above all the other ones. Even though it is in a negative number, it doesn't matte and is till the greatest velocity. The trend also does not go through all of the points, which means the ticker tape experiment is not very accurate. As the ticker tape passes through the timer, the dots are printed on the tape. This means load briefly stops and also the friction is created, which can be the cause of the abnormal results. Therefore I must think of another experiment which can show the full trend (going up and down) and which also does the experiment very accurately.
By looking at both graphs, I can suggest that the mass is travelling at its greatest velocity in the centre of the oscillation. Looking at the graph, it is similar to a sine wave. I know that the greatest velocity is in the middle, because both graphs above show the similar results, which was the maximum velocity was found at the centre of the oscillations.
Evaluation:
From the results we obtained and the graphs that have been analysed, I can evaluate both investigations that the velocity and the period were both successful. In this experiment, all of my predictions are proved to be correct and there were no anomalous results. There were a few points on the graph, which is out of the pattern. However, the investigation went very well. So, there are still things that can be improved and I still had problems with, which could have affected my results.
* In my theory, I said that there were frictions and air resistance, which would slow down the oscillations, and all the springs wouldn't be 100% efficient. So according to that, the oscillations would finally come to an end.
* Hooke's Law is only works under certain conditions. If the force applied to a spring were beyond the elastic limit, the spring would no longer obey Hooke's Law, which can cause inaccurate results.
* In the beginning, the amplitude was a variable, but later I found out that the amplitude could not be a variable, because of the experiment that I did which proved that the amplitude did not affect the time of oscillations. But if the amplitude is very big, because of the heavy mass, the spring may be stretched so much that they no longer would obey Hooke's Law. But this did not happen to my experiments, because it was done very carefully, so that I would not go over the elastic limit. So in the end, the amplitude was not thought of a variable.
* It was impossible to make the springs oscillate 100% vertically. The springs were always waving about, which would have caused inaccurate and abnormal results.
* I would say that the timing was very inaccurate, even though it was done carefully and done as best as I could. It was hard to judge exactly by eyes where one period ends and where the next one starts, and also the slow reactions to click the timer with the human muscles.
* I did not weight the weights myself. But the actual mass of them could be slightly different from what they were labelled, because those were quite old and were used for many years, which could have changed the results.
* It was hard to select two springs, which were the same. It was nearly impossible to select 7 springs which ought to be the exactly the same, but the best were selected in order to get the best results.
For the ticker tape timer experiments, there are a few things we can do to improve it as we discovered that dropping the mass did not prove as good results as when we pulled the mass down and released it. We must think of another method, which can improve the quality of results. This would give a much better curve (trend) with less parts missing. I have conducted a new procedure, using a magnetic sensor and a computer. The set-up and data are shown below, using 2 springs and 2N's of mass. Here are the results, which were collected with this method.
Diagram of the Apparatus:
Results:
Voltage (mT)
Time (s)
0
-6.1
0.05
-6.7
0.1
-7.2
0.15
-7.4
0.2
-7.3
0.25
-6.9
0.3
-6.2
0.35
-5.4
0.4
-4.6
0.45
-4
0.5
-3.5
0.55
-3.1
0.6
-2.9
0.65
-2.7
0.7
-2.7
0.75
-2.8
0.8
-2.9
0.85
-3.1
0.9
-3.5
0.95
-4.1
-4.8
.05
-5.6
.1
-6.4
.15
-7.1
.2
-7.5
.25
-7.5
.3
-7.1
.35
-6.4
.4
-5.6
.45
-4.8
.5
-4.1
.55
-3.5
.6
-3.2
.65
-2.9
.7
-2.7
.75
-2.7
.8
-2.7
.85
-2.8
.9
-3.1
.95
-3.4
2
-3.9
2.05
-4.6
2.1
-5.4
2.15
-6.2
2.2
-7
2.25
-7.5
2.3
-7.6
2.35
-7.3
2.4
-6.7
2.45
-5.9
2.5
-5
2.55
-4.3
2.6
-3.7
2.65
-3.3
2.7
-2.9
2.75
-2.8
2.8
-2.7
2.85
-2.7
2.9
-2.8
2.95
-3
3
-3.3
3.05
-3.8
3.1
-4.5
3.15
-5.1
3.2
-5.9
3.25
-6.7
3.3
-7.3
3.35
-7.5
3.4
-7.2
3.45
-6.7
3.5
-6
3.55
-5.2
3.6
-4.4
3.65
-3.9
3.7
-3.4
3.75
-3.1
3.8
-2.8
3.85
-2.7
3.9
-2.7
3.95
-2.8
4
-3
4.05
-3.3
4.1
-3.7
4.15
-4.3
4.2
-5
4.25
-5.8
4.3
-6.5
4.35
-7.1
4.4
-7.4
4.45
-7.2
4.5
-6.7
4.55
-6
4.6
-5.3
4.65
-4.6
4.7
-3.9
4.75
-3.4
4.8
-3.1
4.85
-2.8
4.9
-2.8
4.95
-2.8
0
-6.1
0.05
-6.7
0.1
-7.2
0.15
-7.4
0.2
-7.3
0.25
-6.9
0.3
-6.2
0.35
-5.4
0.4
-4.6
0.45
-4
0.5
-3.5
0.55
-3.1
0.6
-2.9
0.65
-2.7
0.7
-2.7
0.75
-2.8
0.8
-2.9
0.85
-3.1
0.9
-3.5
0.95
-4.1
-4.8
.05
-5.6
.1
-6.4
.15
-7.1
.2
-7.5
.25
-7.5
.3
-7.1
.35
-6.4
.4
-5.6
.45
-4.8
.5
-4.1
.55
-3.5
.6
-3.2
.65
-2.9
.7
-2.7
.75
-2.7
.8
-2.7
.85
-2.8
.9
-3.1
.95
-3.4
2
-3.9
2.05
-4.6
2.1
-5.4
2.15
-6.2
2.2
-7
2.25
-7.5
2.3
-7.6
2.35
-7.3
2.4
-6.7
2.45
-5.9
2.5
-5
2.55
-4.3
2.6
-3.7
2.65
-3.3
2.7
-2.9
2.75
-2.8
2.8
-2.7
2.85
-2.7
2.9
-2.8
2.95
-3
3
-3.3
3.05
-3.8
3.1
-4.5
3.15
-5.1
3.2
-5.9
3.25
-6.7
3.3
-7.3
3.35
-7.5
3.4
-7.2
3.45
-6.7
3.5
-6
3.55
-5.2
3.6
-4.4
3.65
-3.9
3.7
-3.4
3.75
-3.1
3.8
-2.8
3.85
-2.7
3.9
-2.7
3.95
-2.8
4
-3
4.05
-3.3
4.1
-3.7
4.15
-4.3
4.2
-5
4.25
-5.8
4.3
-6.5
4.35
-7.1
4.4
-7.4
4.45
-7.2
4.5
-6.7
4.55
-6
4.6
-5.3
4.65
-4.6
4.7
-3.9
4.75
-3.4
4.8
-3.1
4.85
-2.8
4.9
-2.8
4.95
-2.8
As you can see above at the results, as the voltage gradually goes up, the time goes up and then goes down again. This gives a graph, which looks like the one below.
Graph:
The unit on the y-axis is called 'Tesla', which means the strength of the magnetic field. Simply, we have been told to analyse these units as Volts. The point where the velocity is at its maximum and minimum are where the mass is travelling the fastest. We know this from previous knowledge, because we are now aware that the base of the oscillation involves electromagnetic induction. The movement of the mass is detected by the magnet sensor, and converted into a voltage, therefore inducing electricity. We also know that the faster an object moves towards a magnet, the more voltage it induces. Therefore, the mid-point of the wave on the diagram represents the mass at the ends of the oscillation, with maximum acceleration and minimum velocity.
The changing magnetic field induces a voltage in the coil. Therefore, we can state that voltage is proportional to the rate of change of magnetic.
From the graph, we can see that the trend looks like a sin wave, however, it is asymmetrical. This is due to the curving magnetic field line. However, in this oscillation, we did not include the mass of the magnet and blue-tack. I feel this could have slightly altered the shape of the wave. To improve this investigation, I would make sure that there was some sort of 'shield' around the apparatus, to protect the sensor from detecting other magnetic sources nearby the experiment.
The advantage of this procedure above, over the ticker-tape method is that we can plot many oscillations and also don't have to worry about catching the mass at the top, and obtaining incomplete data. The disadvantage, is that we cannot conduct a quantitative analysis as it is non linear which is based only on the data produced in the experiment.
Hee-Who Park Oscillations 07/02/01
1AM Coursework
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