Build your own loosely coupled system

This project must be done by individuals.

In this class, we examined the behavior of a pair of oscillating boxes which are connected by a weak spring. We found that if the middle spring is much looser than the side springs, the two blocks will trade their energy back and forth over an extended period of time.

Your job is to build a system which illustrates this phenomenon, measure its properties, and perform a basic analysis. You may receive partial credit for performing the first two of these tasks.

1. Build a system in which two pendula of identical length are connected in some way; they might hang from the same horizontal string or bar, for example.
2. Verify that if you leave pendulum A at rest, but start pendulum B swinging, then over some reasonable period of time, pendulum B slows down and transfers its energy to pendulum A. Adjust the system as necessary to make this happen.
3. Now measure things:
   1. the period of each pendulum, when swung on its own
   2. the time it takes for energy to be transferred from pendulum B to pendulum A, then back to B.

Now comes the analysis. Treat each pendulum as if it were a block of mass m = 1 kg, connected to a single spring of force constant k. Based on the period of each single pendulum, what is the value of k?

Now look at the coupling between the two motions. Based on the time it takes for one full cycle of transfer of energy (B to A and back to B again), and treating the connection between the two pendula as an ideal spring of force constant k_c, compute the value of k_c.

Hand in a sheet of paper, showing all your work. Provide photographs of your device, either in hardcopy or electronically.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.