# Homework Help: A Simple Harmonic Motion Problem

1. Jul 25, 2010

### Faux Carnival

1. The problem statement, all variables and given/known data

[PLAIN]http://img441.imageshack.us/img441/6951/physics.gif [Broken]

As shown in the figure, one end (O) of a uniform rod of length L and mass M is pivoted to a wall. Two horizontal springs with force constants k1 and k2 are attached to the other end (P) of the rod. When the rod is aligned exactly along the vertical axis, the system is in equilibrium.

a) Find the period of small oscillations of the rod.
b) Assume that the initial angle the rod makes with y-axis is a small angle θ and the initial velocity 0. Find the velocity of the end point P of the rod as it passes through the equilibrium position.

2. Relevant equations

Moment of inertia of a rod relative to its end: I = 1/3 ML2

3. The attempt at a solution

I think I have a solution but it is too long and complex. I doubt it's correct. Any help appreciated.

Last edited by a moderator: May 4, 2017
2. Jul 25, 2010

### Swap

Moment on the rod due to the spring is 2kl^2*theta. Equate it with I(alpha) then u will gte alpha and hence omega. From here u can proceed easily to find the period

3. Jul 25, 2010

### Faux Carnival

That's what I did. But I added the moment from the mass of the rod too.

So k1L2θ + k2L2θ + MgLθ/2.

That's equal to Iα. (α being the second derivative of θ)

(k1L2θ + k2L2θ + MgLθ/2) / I is therefore w2.

That's part a. For part b, wmax = wθ and Vmax = wθL.

[PLAIN]http://img375.imageshack.us/img375/6378/captureoj.jpg [Broken]

Last edited by a moderator: May 4, 2017
4. Jul 25, 2010

### Swap

yes u r correct....

5. Jul 25, 2010

### Faux Carnival

Thanks a lot Swap.