Physics Coursework: To investigate the Oscillations of a mass on a spring

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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.
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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. ...

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