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A rigid bar with a mass M and length L is supported by a spring and a viscous damper as shown.

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The explanations are in the attached PDF file.

For possible reference by Brainmass, I also past in the TEX script from which the pdf was produced - you do not have to read it as you already have the pdf file.

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Here is the plain TEX source
centerline{bf Rattling bar}

The moment of inertia of the bar about its fixed end is $I = ML^2/3$.
When the bar is inclined at small angle $theta$ to horizontal clockwise, the point where the spring is attached has vertical displacement approximately $atheta$,
and the point where the spring is attached has ...

Solution Summary

A rigid bar with a mass M and length L is supported by a spring and a viscous damper as shown.

$2.19