What Is the Oscillation Period of a Rod Attached to a Spring?

[bcjochim07]

Homework Statement

A 200g uniform rod is pivoted at one end. The other end is attached to a horizontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rod's oscillation period? You can assume that the rod's angle from the vertical is always small. The rod's length is 20 cm and the spring's constant is 3N/m.

Homework Equations

The Attempt at a Solution

Without the spring the rod's angular frequency would be sqrt[(.200)(9.80)(.10m)/(.0027kgm^2) Then I could go to period. Will someone tell me how I can get the period for the spring? The problem is I am used to doing problems with just a spring and a block, but I am not quite sure how to deal with the extended object. Would I just use omega= sqrt [k/m] with mass .200kg and k = 3.0 N/m? Then I could go to period, and maybe add the two period together?

 

[kamerling]

For a simple harmonic oscillator the restoring force is F = ma = -kx. what is the total restoring force for the pendulum string combination? If that is in the form -kx you can use the equaton for the period of a simple harmonic oscillator.