Asimple pendulum consists of a mass m attached to a light string of length l. when at rest it lies in a vertical line at x = 0. the pendulum is driven by moving its point of suspension harmonically in the horizontal direction as ξ = a cos ωt about its rest position (x = 0). there is a damping force fd = −bv due to friction as the mass moves through the air with velocity v. (a) show that the horizontal displacement x of the mass, with respect to its equilibrium position (x = 0), is the real part of the complex quantity z where m d2z dt2 + b dz dt + mω2 oz = mω2 oaeiωt and ω2 o = g/l. (b) assuming a solution of the form z = aei(ωt−δ), show that the phase angle δ between the driving force and the displacement of the mass is given by tan δ = γω ω2 o − ω2