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

If the damping constant of a free oscillator is given by b=2 m ω0, the oscillator is said to be critically damped. Show by direct substitution that in this case the motion is given by

x=(A+Bt)e^(−βt)

where A and B are constants.

A critically damped oscillator is at rest at equilibrium. At t = 0 the mass is given a sharp impulse I. Sketch the motion. Calculate the maximum displacement.

Data: I = 11.1 Ns; m = 1.1 kg; k = 18.2 N/m.

2. Relevant equations

[itex]\beta[/itex]=b/(2m)

3. The attempt at a solution

Two things I find wrong here:

1: since x(0)=0 and v(0)=0 it implies that A and B= 0 which is wrong so that must mean I plays a role, obviously.

2. I do not know how to incorportate the impulse into x(t)

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# Critically Damped oscillator

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