For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation m y double prime (t )plus b y prime (t )plus ky (t )equals 0my′′(t)+by′(t)+ky(t)=0. (a) Find the equation of motion for the vibrating spring with damping if mequals=2020 kgkg, bequals=240240 kg divided by seckg/sec, kequals=740740 kg divided by sec squaredkg/sec2, y(0)equals=0.10.1 mm, and y prime (0 )y′(0)equals=minus−0.40.4 m divided by secm/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point? (c) Find the frequency of oscillation for the spring system of part (a). (d) The corresponding undamped system has a frequency of oscillation of approximately 0.9680.968 cycles per second. What effect does the damping have on the frequency of oscillation? What other effects does it have on the solution? (a) y (t )y(t)equals=0.1 e Superscript negative 6 t Baseline cosine t plus 0.2 e Superscript negative 6 t Baseline sine t