(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to figure out the normal frequencies (or eigenfrequencies) of a system of two simple pendula (call them A and B), connected with by a massless rigid rod at an arbitrary distance from the pivot point or the mass. That is, the pendula are not connected at their masses, but at some point along the strings.

2. Relevant equations

...?

3. The attempt at a solution

My textbook only deals with the case where the pendula are connected at their masses. But, to find the normal frequencies of that system, they first solved a system differential equations, which described the position of A and B as a function of time. Also, they assumed the angle made with the vertical was small enough so sin ([tex]\vartheta[/tex]) [tex]\approx[/tex] [tex]\vartheta[/tex]. Further, they assumed that the amplitudes of the oscillations were small enough so the motion of the pendula could be looked at in the horizontal direction only.

I was able to follow the derivation of the problem in the textbook, but I'm having trouble picturing how the system would operate. Do you consider the part of the system above the rigid rod to be a single pendulum, with two strings? And the parts below the rigid rod are considered regular pendula, but attached to a moving structure?

Can someone give me a hint?

Oh, and I'm pretty sure there are only 2 normal frequencies: optical and acoustic...

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edit:

Also, the coupling rod is positioned such that there is no twisting of the system. it is positioned high up enough along the strings so this effect can be ignored.

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# Homework Help: Normal frequencies of 2 pendula connected with a massless rigid rod

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