# Coupled oscillation: time interval between maxima

## Homework Statement

I calculated $$T_o$$ to be 1.27 seconds and $$"T_o"'$$ to be 1.23 seconds, each representing a normal mode of oscillation. These are correct according to the text.

Here is the question: what is the time interval between successive maximum possible amplitudes of one pendulum after one pendulum is drawn aside and released?

## The Attempt at a Solution

I'm not even quite sure how to begin this problem, or what it is asking precisely. Is this suggesting that both modes of oscillation are superimposed? If this is the case, the superimposed period would be 1.25s.... where am I going wrong here?

Last edited:

vela
Staff Emeritus
Homework Helper
What are the two modes of oscillation, and what initial conditions would you need to excite each one?

The first mode starts with equal displacement for both pendulums, both oscillate with natural frequency $$\sqrt(\frac{g}{l})$$. The second mode starts with equal displacement but opposite signs for the pendulums, both oscillating with frequency $$\sqrt(w_0^2 + w_c^2)$$.

vela
Staff Emeritus
Homework Helper
Right. The initial condition given doesn't excite just one mode, so the motion will be the superposition of the two modes, which have different frequencies. What happens when you combine two oscillations with different frequencies?

You get a beat with a frequency of each pendulum equal to the average of the two normal frequencies = ~ 0.80 hz = ~ 5.02 rad/s.

vela
Staff Emeritus