- #1

dumbdumNotSmart

- 41

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## Homework Statement

You got a plate hanging from a spring (hookes law: k) with a viscous force acting on it, -bv.

If we place a mass on the plate, gravity will cause it to oscillate.

Prove that if we want the plate to oscillate as little as possible (Crticial damping, no?), then $$b=2m \sqrt{(g/Δx)}$$

## Homework Equations

$$F=ma $$

## The Attempt at a Solution

I cannot for the life of me get the differential equation right. Given the conditions I assume they want me to find b for a critically damped system (also answer looks like so). This is my best try

$$ma=-bv +mg -kx$$

Since g is not accompanied by x, dx or d

^{2}x it will be part of the particular solution, not the homogenous. What am I missing here?