(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)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Critically Damped oscillator

**Physics Forums | Science Articles, Homework Help, Discussion**