Two Discs on a Rod - Solving Normal Freqs & Modes

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Homework Help Overview

The discussion revolves around a problem involving two discs mounted on a rod, focusing on calculating their normal frequencies and modes of oscillation. The original poster describes the setup and their initial attempts at formulating the kinetic and potential energy expressions related to the system's motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive expressions for kinetic and potential energy based on the angles of rotation of the discs. Some participants question the validity of the energy expressions and the implications of the initial conditions on the motion of the discs.

Discussion Status

The discussion is ongoing, with participants exploring the nature of the normal modes and the conditions under which one disc might receive all the kinetic energy. Hints have been requested rather than direct solutions, indicating a desire for guidance on how to approach the problem further.

Contextual Notes

There is a specific mention of initial conditions where one disc starts with an initial velocity, raising questions about energy transfer and motion dynamics. The original poster also expresses uncertainty about their calculations and seeks clarification on the setup.

Feynmanfan
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Dear friends,

I'm having trouble with this problem, I don't know if I'm doing it right, I'd be grateful if you could advice me.

Two discs, each of mass M and radius R, are supported with equal
separation along a slender rod to which they are rigidly fastened at
their centers as shown in the picture I attached below.

I need to calculate the normal frequencies and normal modes.

This is what I've done:

T(kinetic energy)=1/2*1/2MR^2(theta1^2+theta2^2)
V(potential)=1/2*k(theta1^2+theta2^2+(theta1-theta2)^2

Where theta is the angle the disc turns. Does this make sense?

THanks!
 

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well,

If what mentioned above is right, I found out that either in phase or counterphase are the system's normal modes.

The thing is that, at the beginning both discs start from 0 but disc number 2 has an initial velocity u. I am asked to describe the motion and calculate how long it will take the first disc to get all KINETIC ENERGY.

Don't solve the problem for me, but just give me a hint what I should do.

THanks
 
is it possible that disc 1 can receive all the kinetic energy?
 
please. I need help
 

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