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JordanGo
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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