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## Homework Statement

A mass of 1000 kg drops from a height of 10.0 m onto a platform of negligible mass.

It is desired to design a spring and damper on which to mount the platform so that it

will settle to a new equilibrium position 2.00 m below its original position as quickly

as possible without overshooting.

Find the spring constant k and the damping parameter

if the system is critically

damped.

## Homework Equations

ω^2(frequency squared)=γ^2(damping parameter squared)

E=U=mgh at equilibrium

E=1/2kA^2

x(t)=(A1+A2t)e^(-γt)

## The Attempt at a Solution

First, I solved for energy:

E=U=mgh=19400

Then for the spring constant:

k=2E/A^2

But now I need amplitude, so this is where I taking a shot in the dark:

x(t)=(A1+A2t)e^(-γt)

Now I was thinking to say that if t goes to infinity, x is 2, but it gave me no information... I need help! please and thank you