Two Discs on a Rod - Solving Normal Freqs & Modes

[Feynmanfan]

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!

 

[Feynmanfan]

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

 

[Feynmanfan]

is it possible that disc 1 can receive all the kinetic energy?

 

[Feynmanfan]

please. I need help