Understanding Undamped Oscillations

[jonnyboy]

[SOLVED] Undamped oscillations

In the diagram below, the disk is mounted vertically on ideal bearings through its center mass. If the system is disturbed from its equilibrium position, determine the frequency of the undamped oscillations. I = 4kg m^2

This one I have no clue about. We rushed through frequencies and oscillations in less than an hour on our last class. Please just let me know what's going on here and how I should tackle it. Thanks

 

[Astronuc]

Undamped means that the system has no friction (in the axis of the pulley or springs) and no damping term in the differential equation which relates the force inducing the motion to the displacement in the springs. But there is friction between the wire, cable or string and the pulley. Now this seems a bit tricky because the pulley rotates while the springs displace longitudinally (along their axes), but the displacements of the springs can be related to the angular displacement of the pulley.

One needs to develop an equation that has the form, I$\theta$'' + k$\theta$ = 0, where the angle is the angular displacement from the pulley's position when both springs are at their equilibrium position, i.e. when both springs apply equal force.

 

[CompuChip]

How do you mean; bump?
You already have a response, is it no good, or don't you understand it?