Critically damped oscillator If the damping constant of a free oscillator is given by γ = 2ω0, the system is said to be critically damped. (a) Show by direct substitution that in this case the motion is given by
![1868_2e55d04a-3205-41ee-84e2-6fd0334f3720.png](https://secure.tutorsglobe.com/CMSImages/1868_2e55d04a-3205-41ee-84e2-6fd0334f3720.png)
where A and B are constants. (b) A critically damped oscillator is at rest at equilibrium. At t = 0 it is given a blow of total impulse I. Sketch the motion, and find the time at which the velocity starts to decrease.