Question: I am doing some physics coursework and cannot find what I'm looking for. My coursework title is "How does the mass on the end of a spring affect the time period of the spring?" We put different masses on the end of a spring and then extended the spring an extra 2 cm (to increase the tension apparently). We then let it go and timed how long 10 oscillations of the spring took, we divided it by 10 to get the time period of 1 oscillation, we then repeated this with other masses being put on the end of a spring. I have lots of notes which I just don't understand! I would be really grateful for any help you could give me. I cannot seem to find anyone else who is doing the same coursework either, the coursework needs to be handed in soon too! I have been trying for a long time to understand.
1. Suspend
your spring from a support.
2. Put an initial load on the spring – say 100g
3. Pull the
spring down a little way (about 5 cm although the actual distance does not matter) and then
let go.
4. Time 10 oscillations (you can start at any time but best at either the top or
bottom of an oscillation.
5. Divide by ten to get the time for one oscillation.
6. Add
another 100 g (50g if you can) and repeat the procedure for another five or six masses. You
really need six to get a graph, eight is even better. It is not necessary to pull the mass down
the same distance each time because the period (T) does not depend on the amplitude as
long as the amplitude is not too big.
7. Make a table of the mass and the time for one
oscillation
8. Plot a graph of mass (M) (y axis) against time (T) (x axis)
This should
give you a curve, the T values increasing faster than the M values.
9. Plot a second
graph of (M) (y axis) against T squared (x axis)
This should give you a straight
line.
N.B You must not get the spring to extend beyond its elastic limit. The way to check
this is to make sure that the spring goes back to its original length after each load.
The
theory of this is really A level but I will give it you all the same. Most A level textbooks have it
and it is also on the web site. Don't worry if you do not follow it yet.
Theory of the
oscillation of a mass on a helical spring
Consider a mass m suspended at rest from a
spiral spring and let the extension produced be e. If the spring constant is k we have: mg =
ke
The mass is then pulled down a small distance x and released.
The mass will
oscillate due to both the effect of the gravitational attraction (mg) and the varying force in the
spring (k(e + x)).
At any point distance x from the midpoint: restoring force = k(e + x) -
mg
But F = ma, so ma = - kx and this shows that the acceleration is directly proportional
to the displacement, the equation for s.h.m.
The negative sign shows that the
acceleration acts in the opposite direction to increasing x.
From the defining equation for
s.h.m. (a = - w2 x) we have w =k/m=g/e and therefore the period of the motion T is given by:
Period of oscillation of a helical spring (T) = 2p(m/k)1/2