l. (25 points) A mass of 1.5 kg rests on a horizontal table and is attached to one end of a spring of spring constant 150Nm'1. The other end of the spring is moved in the horizontal direction according to :1: = acoswt where a = 5 x 103 Ill and w = ared/s. The damping constant b = 3.0N-m"s. Determine the amplitude and relative phase of the steady state oscillations of the mass. Show that if the applied frequency were adjusted for resonance, the mass would oscillate with an amplitude of approximately 2.5 x 10-?m