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

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Introduction

Hee-Who Park        Oscillations        07/02/01

11AM        Coursework

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.

Middle 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) 1 4 - 8.28 8.35 8.31 8.32 8.315 0.8315 2 4 - 10.66 10.81 10.89 10.65 10.7525 1.07525 3 4 - 14.25 14.26 14.19 14.32 14.255 1.4255 4 4 - 14.70 15.06 15.10 15.26 15.03 1.503 5 4 - 20.44 20.53 20.31 20.48 20.44 2.044 6 4 - 18.47 18.74 18.62 18.76 18.6475 1.86475 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:

Conclusion

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.

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