(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

John the door-stopper man sells and installs door-stoppers. He prides himself as being the world's best stopper and guarantees your money back if you can install a better stopper than him.

John's secret to door-stopping is that he remembers from his lectures that the best way to stop doors is by fine tuning the stopper such that it is critically damped.

2. Relevant equations

Trick John (and ask for your money back) by showing him that if you open a critically damed door and release it without also pushing it, it will never ever close again.

3. The attempt at a solution

The equation of motion is a second order differential equation in the form: mx"+cx'+kx=0; then let x=e^(zt);

I realise that for a critically damped system, the determinent for the characteristic equation z^2 + (c/m)z + (k/m) = 0 equals to (c/m)^2 - 4(k/m) = 0;

Then solving for x to find the equation in the form of x(t) = (A + Bt)e^(-t(k/m)^0.5)

However, the problem is that this solution converges to the equilibrium position under critically damped conditions.

How can I show that the door will never close again?? (It seems impossible!!)

Your help is much appreciated!

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# Homework Help: Critically Damped Harmonic System

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