Homework Help: Weakly Coupled Oscillators

1. Oct 25, 2016

Zanatto

1. The problem statement, all variables and given/known data
Two simple pendulums os equal lenght L=1m are connected with spring with a spring constant K=0,05 Mg/L. The pendulums are started by realeasing one of them from a displaced position. The subsequent motion is characterized by an oscillatory energy exchange between the pendulums. What is te period of this transfer?

2. Relevant equations

3. The attempt at a solution
In this situation, as a pendulum is displaced and the another is static, I suppose that when the amplitude of pendulum 1 is a maximum, the amplitude of pendulum 2 is minimum, because the result is displaying "beat" frequency. That's correct?

2. Oct 25, 2016

BvU

3. Oct 25, 2016

Orodruin

Staff Emeritus
Yes. When the amplitude of one of the pendula is zero, the amplitude of the other is maximal. This follows directly from energy conservation.

4. Oct 25, 2016

Zanatto

Well, just to get rid of the doubt.

Them, starting from the equation of position, and I found that the maximum values of the amplitude for the pendulum 1 occurs when:

επ(t/T) = nπ ---> t/T = n/ε

The time between maxima is T/ε, inversely proportional to the coupling spring constant.

And for the pendulum 2 when:

επ(t/T) = (2n +1)* π/2 ---> t/T = (2n+1)/2ε

Them, I stuck in here. Can I relate that with period of transfer in the oscillatory energy exchange in some way?

5. Oct 25, 2016

BvU

Good. So what's this exercise ? In a chapter on differential equations, on Larangian mechanics, a lab instruction preparation perhaps ?

The motion described is asymmetric and one can expect the pendulum that's initially immobile to start swingning too.
There are simple modes possible where there is no transfer; can you guess which ? Wht are their frequencies ?