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Investigation on the effect of the stiffness of a spring on the oscillation period.

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Introduction

PHYSICS COURSEWORK

Investigation on the effect of the stiffness of a spring on the oscillation period.

AIM

To investigate how the stiffness of a spring effects the period.

APPARATUS

Clamp and stand, stopwatch, springs and mass (constant).

METHOD

A clamp and stand will be set up with a combination of springs attached to it and hanging from the set of springs will be a weight carrier. The weight carrier will hold the masses, and this mass will always be constant to make it a fair test because we are testing the springs not the weights. The springs are the variables. The spring combinations will be varied and this is so we can control the strain force exerted by the spring (stiffness). For example, two springs in parallel have got twice the amount of stiffness as a single spring with springs that have equal stiffness. This is because if two springs are in parallel then they each share the weight attached to them so obviously the spring won’t be extended as much as the single spring, probably only half as far as the spring will stretch for the single spring. The opposite of this happens when the springs are in series.

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Middle

Spring Combination

Spring constant N/m

4 in series

5.25

3 in series

7

2 in series

10.5

2 in parallel, 1 series

14

2 in parallel

42

3 in parallel

63

SINGLE SPRING

21

The stiffness for a single spring is 21, so then you can see the spring stiffness for the other combinations in relation. For example, for 2 in series, the spring constant is half of a single spring, 3 in series, the spring is a third of that of a single spring, 4 in series, and it is a quarter. For 2 in parallel, the spring constant is double that of a single spring, for 3 in parallel it is triple. For 2 in parallel and one series, the spring constant is 2/3 of a single spring. This proves what I said in the planning.

I predict that the stiffer the spring will be, the shorter the oscillation period will be also.

The equation that connects spring stiffness and oscillation period is:

image02.png

We can ignore 2 because it is constant, so therefore what we are left with means that the period is inverse proportional to the square root of the spring stiffness.

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Conclusion

        The results were quite good because if you look at the table the results are all very similar, so this shows the timing was quite good. Also, averages were taken, so this gave a more accurate figure. The figures used were all to two decimal places so the figures used were actually quite precise.

        The errors will most probably have been a cause of human reaction time. Humans can’t time the oscillations so precise because they’re reactions aren’t perfect. This is why some results may have been slightly out of place. However, they weren’t that out of place that it affected the investigation in any major way. The only other way, human error could be eradicated, is by using some sort of mechanical way instead.

        Other work that could be done is to investigate how changing the masses effects the oscillation period. The same apparatus could be used too and the same formula would apply.

image02.png

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