METHOD-I set up my simple pendulum like the one shown in the diagram. Firstly I took a piece of string 50cm long and attached securely a small bob at the end of the string.
The thread is secured between the two halves of a split cork held securely in a clamp mounted on a stand. The length of the pendulum is carefully measured from the place where the thread emerges from the cork to the middle of the pendulum bob. This would ensure that the bob swings from a single fixed point.
Time period of a pendulum is the time taken to complete one full oscillation. I need to record the time period but it is too short, so I will time 20 periods and then divide the final time by 20 to give me the time period of the pendulum.
Timings for twenty complete oscillations are started and stopped as the pendulum passes through the mid point. As the thread passes the mid point the stopwatch is started and counting is started. The pendulum will swing to one side, then back through the centre and to the other side. When it passes the centre again ‘1’ is counted for the first complete swing. This is repeated until 20 oscillations and the time is stopped as the thread passes the 20th oscillation.
Then to find the time of one oscillation divide the time taken for all 20 oscillations by 20. The angle of amplitude must not be very big because then the gravitational potential energy will increase tremendously. Each time I increase the thread length by 10cm and measure another reading.
Formula for time period of a pendulum is:
T=2 Π√l/g
T²=4Π² l/g
g=4Π² l/ T² …………..(1)
Where
● Π = 3.14
● l = length of the thread
● g = acceleration due to gravity
● T = time for one oscillation or the period of the pendulum
-
G= ΔT² G stands for gradient
Δl
G T² ………………(2)
From (1) and (2)
We get g = 4Π² /G
Fair test: to make the experiment as fair as possible the same bob and apparatus were used for each experiment. The length of the pendulum was measured from the base of the split cork to the middle of the metallic bob. The angle of amplitude at which the bob swings should be the same.
Safety: if the experiment were not carried out safely there would have been possibilities of accidents occurring. In order to prevent such accidents occurring I had to keep a few simple guidelines into consideration: -
- Keep my table clean and tidy before starting.
- Care will be taken not to let the bob come into contact with anything whilst swinging.
- When the bob is swinging take care that it does not hit someone.
- The stand should be kept clearly and firmly secured to the table otherwise it could fall over and hit someone.
- Excessively large swings should be avoided.
OBTAINING EVIDENCE
I used the method proposed in my plan, taking two readings of each value and measuring the time taken for 20 oscillations rather than for one. I was careful to use accurate measurements in order to obtain sufficiently accurate results, for example: the string was measured with a meter ruler to the nearest mm, to ensure that each measurement had a difference of 10cm.
READINGS OF THE EXPERIMENT
* Average time = T1 + T2
2
* One swing = average time
20
●Observation-I will measure the changes in time period when the length of the string of the pendulum increases.
ANALYSIS
The graph shown on the above page which has length (cm) on the horizontal axis (x-axis) and time (seconds) on the vertical axis (y-axis) clearly shows a straight line with a positive gradient. This indicates that as the length of the pendulum is increased the time period of the pendulum will also increase. This implies that (time period) ² is directly proportional to the length of the thread, i.e. if the length of the string will double then the (time period) ² would double.
From my graph I have got most of the points passing through the line of best fit. So I can see that my results are correct.
After drawing the graph I found the gradient for it I selected two best points, which are going through the line. After selecting the two points I found the gradient of the graph.
G= ΔT²
Δl
ΔT² = change in time period
Δl = change in length of the thread
Method of calculating the acceleration due to gravity
G = ΔT²
Δl
ΔT² = 3.9-3.5
= 0.4
Δl = 100-90
= 10
G = 0.4 = 0.04
10
g = 4Π² /G = 4(3.14) ²
0.04
= 4* 9.8596
0.04
= 985.96cm/s²
= 9.85m/s²
CONCLUSION
Table of results and graphs drawn from my experiment were extremely similar to what I had predicted, showing that my experiment was successful.
From the graph that I have produced I can clearly see that there is a positive correlation between the length of the thread and the time taken for one oscillation. This is in line with my prediction. My graph showing (time period) ² against length is a straight-line graph meaning period² is directly proportional to the length of the pendulum. So I can say that the length of the thread affects the period of a pendulum. As the length of the string increases the period of the pendulum also increases.
After drawing my graph I found the gradient of my graph. I got G= 0.04 where is the gradient. And then I found the acceleration due to gravity (g) using the formula T=2 Π√l/g. then I got g= 9.85m/s² which again proves my prediction to be correct.
EVALUATION
From looking at my results on the table, graphs and comparing them to the formula I concede that the investigation was successful.
There is a possibility for an inaccuracy in my project and that is when I left the bob from my hand, there is no surety as to whether the stopwatch was started at exactly the same time when the bob was left.
Also it was not entirely possible to get completely accurate results, as there was not an easy way to recognize where to stop the clock.
If I was to repeat the experiment I would make sure there were two people doing the experiment so that when one leaves the bob the other person starts the stopwatch exactly at the same time so that there were no inaccuracies.
Secondly I would prefer for there to be some indication of one oscillation, if I were to repeat this investigation so that I know when to stop the stopwatch.
But overall according to me the experiment was successful as it matched with my prediction and it gave me evidence that could be said to be reliable as it matches with the information found in physics textbooks about the formula and the shape of graph. I also got g= 9.85m/s² which is nearly equal to Newton’s result.