Record Clamp

Record Clamp

Oscillations of a meter rule practical Q?

I'm doing a practical tomorrow where a meter ruler is attached on two strings , to two clamp stands and is twisted . The time for 10 oscillations is recorded . This is then repeated for different distances between the stands . I've got two questions ,

1. What are the main Physics principles that apply
2. Does anyone know what the relationship between distance and time should be ?

For errors these will mainly be in the stop clock and the meter rule and the measurments I take ? Is this correct ?
Thanks .

This is an example of torsional oscillations (that is, twisting), and simple harmonic motion (SHM). The main physics principles are: SHM, moment of inertia, restoring couple. I doubt if you will become involved in the theory in any great depth, especially the mathematics. Essentially, you ca put the ruler in an "equilibrium position" in which the two strings are in the same vertical plane and the meter ruler is at rest. If you then disturb it slightly by moving rotating the ruler say 20 degrees, it will oscillate back and forth. The mathematical model that approximates this will be of the type: Restoring force is proportional to displacement. (In your case, it will be restoring couple proportional to instantantaneous displacement.) The frequency of oscillation will go down as the distance between the strands is reduced, and I expect you will be asked to plot the relationship and see if it is a power law and what the power index is (i.e what is n in the equation frequency = k x (distance between threads)^n.

The frequency should be almost independent of amplitude and mass of the ruler. However, it will depend on the "radius of gyration" (=mass/moment of inertia), so if you stick masses on the ends of the ruler the frequency will be lower.

You will probably treat this as a practical rather than theory, so you will want to identify sources of error. I would expect the main one being the uncertainty in getting the time of ten oscillations, because this requires eye/hand co-ordination in spotting the start and end time. Plan first about exactly what you are going to vary and what you are going to measure, and whether or not you are plotting a graph as you go along. Have fun!

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