Hypothesis
I believe that the more weight you put on the spring, the more time it will take to make an oscillation. To explain this I will start off at the beginning. According to Hooke’s Law the extension is directly proportional to the force loaded onto it. The graph below shows the load and the extension. The line is straight meaning x=y or extension is directly proportional to load.
And therefore that if you doubled the weight you added to the spring then the extension of the spring will double as well.
However this will only happen up until a certain point, because after that the spring will not revert to its original shape. This point is called the elastic limit. The graph below shows the elastic limit of a spring. As you can see, at a certain point Hooke’s law fails to work. It starts off, with extension being directly proportional to load until it reaches the elastic limit where the spring extends more than it would if extension was directly proportional to load. This is where the spring starts to stretch out of shape and will not go back to its original state.
As my investigation is into the time a spring takes to ‘bounce’ 10 times I will use the information I have just given to explain my hypothesis for the experiment.
My theory is that if a spring extends further then it will take longer to ‘bounce’.
I think that this is because when you add weight to the spring, you give it more potential energy. When you let it go it releases kinetic energy. It will travel further, the more potential energy it has. The spring then needs energy to revert back to its original shape. Because it needs energy it takes more time to get back to the original position. If you add more weight to the spring then it will need more energy to get back. The more weight you add, the more energy is needed and so the slower it takes to get back. This means that if you gave each added weight more pull to start off with, they would probably all take the same amount of time to revert to their original position.
Results
Conclusion
As more weight was added the time it took to oscillate increased i.e. 100g took 3.84 seconds to oscillate whereas 500g took 8.89 seconds to oscillate. The weight added is proportional to the time but not directly.
My hypothesis said that the more weight you add to the spring, the longer it would take to oscillate ten times. As this is shown in the results I think my hypothesis is correct.
According to the laws of simple harmonic motion for mass on a spring5, the formula for the period of one oscillation is:
T=2π √m
K
Where
T= Time taken for one oscillation
m= Mass added to the spring
k= The tension required to produce a unit extension (the spring constant)
Using this formula I can now find the formula for 10 oscillations:
10T= 20π √m/k
As we already know the time taken for the oscillations we do not need to use this formula apart from to show why T α m.
The constants in this equation are: 10,20,π,√k. The only variables in the equation are T and √m, as the time changes so does the mass but everything else stays the same.
As m gets bigger so √m/k gets bigger meaning 20π√m/k gets bigger and so T increases according to the equation.
I pointed out earlier that T α m but not directly.
Something else I managed to conclude was the constant of K, I managed to rearrange the equation to work out K.
T=2*pi* mass/K
0.384^=2^*pi^*100/K
0.147456=4*pi^*100/K
0.147456*K=3947.6
K=2677.3
Evaluation
I feel the experiment went very well, we had no anomalous results and we had no safety errors. However there were a few things we could have done that I feel could have pushed to a more accurate and fair experiment. We should have used electronic computer aided timers that would have stopped bang on the tenth oscillation, however we had to stop it by hand with a digital timer. We could also have used a different measuring device to measure the distance we pulled the weight down by to create a fairer test and thus eliminating bias. However my results agreed with my conclusion and helped me to prove my theory.