(a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion of the damped harmonic oscillator of mass M, with damping constant and spring stiffness k is Eqn.1.Mdt2d2x(t)+dtdx(t)+kx(t)=0 (b) Using the trial solution method and De Moivre's theorem, show that x(t)=e2M(C1cos1t+C2sin1t),where1=(2M)2Mk (c) What is the solution of Eq. 2 for the case =0, interpret this solution physically. (d) Using the expression for x(t) in part (b), find an expression for the initial velocity of the damped oscillator, with the following parameters, M=1,=2,k=10