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## Homework Statement

A mass of 1000 kg drops from a height of 10 m on a platform of negligible mass. It is desired to design a spring and dashpot on which to mount the platform so that the platform will settle to a new equilibrium position 0.2 m below its original position as quickly as possible after the impact without overshooting.

a)Find the spring constant k and the damping constant b of the dashpot.

b)Find the time required for the platform to settle within 1 mm of its final position.

## Homework Equations

$$mg=kx$$

$$m\ddot{x}+b\dot{x}+kx=mg$$

$$\omega=\sqrt{\frac{k}{m}}$$

$$\gamma=\frac{b}{2m}$$

Answers:

a) ##k=49000kgm/s^{2}##, ##b=70700 kgm/s##

b)##0.076sec##

## The Attempt at a Solution

I am having trouble finding the value of ##b##. I assumed that since the question asks for the quickest amount of time without overshooting, this would be a critical damping problem with ##\omega=\gamma## but when I solve there is overshooting. The only way that I am able to get the answer for part b) is to take away from forcing function ##mg##.