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hils0005

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**[SOLVED] Diff EQ spring question**

## Homework Statement

a)IF a mass of 0.5kg is attached to a spring with a spring constant of 5(nt/m) and then receives a blow to dislodge it from its equilibrium position, then what is the resistive force coefficient (gamma) if the system is critically damped?

b)what is the general solution for the position u(t) of the mass?

## Homework Equations

mx''=-kx-ax'+f(t)

x''+ (a/m)x' + (k/m)x = F(t)/m

m=.5kg

k=5N

gamma=? (a/m)x' ?

## The Attempt at a Solution

I don't understand what "critically damped" means?

x"+(a/.5)x'+10x=0

I really don't know how top start this, any help would be appreciated