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
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.