- #1
kraigandrews
- 108
- 0
Homework Statement
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.
Homework Equations
[itex]\beta[/itex]=b/(2m)
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)