Problem 3 (40 points): Assume the damped harmonic oscillator for a body with mass m, and corresponding total force F = kx bv, (5) where k is the spring constant, b the drag coefficient, v the velocity and z the spring dislocation. (a) Find the general solution for the position of the mass z (t), i.e., solve the equation F = m'ng'. (b) Find the particular solution assuming initial conditions z ( = 0) = 2 and i +o = 0 (10 points). (c) Find the particular solution assuming initial conditions z ( = 0) = 0 and 4| _ = v (10 points). Analyze and describe the difference between the oscillatory movement of the general solution [obtained in item (a)| for b/(2m) > \\/k/m and b/(2m)