Problem 4 (40 points): Assume the driven (and damped) harmonic oscillator for a body with mass m, and corresponding total force F = kx bv + Fysin (w,t), (6) where k is the spring constant, b the drag coefficient, v the velocity, x the spring dislocation, and F{ the external force with oscillatory frequency w,. (a) Find the general solution for the position of the mass z (t), i.e., solve the equation F = m'f:T?. (b) Find the particular solution assuming initial conditions z(t=0)=2xzand 't:O = 0 (10 points). (c) Apply the long time limit, defined by > b/2m, within the solution of item (b) interpret the obtained result (10 points). (d) For (c), show what is the resonance frequency of the system, i.e., for which external frequency w, will the system acquire the largest amplitude? (10 points)