Vertical Oscillation Frequencies of a Hanging Rod: Exploring Normal Modes

[benij_chaos]

I Have a question that is bugging me because I can't get the answer out here's the question:

A uniform rod of length a hangs vertically on the end of an inelastic string of length a, the string being attached to the upper end of the rod. What are the frequencies of the normal modes of oscillation in the vertical plane.

Any help would be appreciated thanks

 

[Gokul43201]

benij, it is required that you show your thoughts/efforts when asking for help with coursework/textbook problems.

 

[benij_chaos]

I set the problem up with two angles, one that joins the string to the vertical and one that joins the string to the rod. My problem comes in not knowing how treat the mass in the question. I have tried dividing it up into two parts and that does not seem to work. I am effectively stuck before I am started.

 

[Gokul43201]

Can you find the velocity of the center of mass of the rod, in terms of the lengths and angles (and their derivatives)? From v(COM) and the angular velocity about its top end, you can then write down the total kinetic energy term, T.

PS: I don't know what 2 masses you are talking about. The string is massless.