(A) A damped oscillator is described by the equation
m [(x)\ddot] = -b [(x)\dot] - kx .
What is the condition for critical damping? Assume this condition is satisfied.
(B) For t < 0 the mass is at rest at x = 0. The mass is set in motion by a sharp impulsive force at t = 0, so that the velocity is v0 at time t = 0. Determine the position x(t) for t > 0.
(C) Determine the maximum displacement of the mass for t > 0.
(D) Suppose m = 1 kg and v{k/m} = 2p rad/s. Calculate the maximum displacement for t > 0, as a function of v0. Hand in an accurate graph of xmax versus v0.