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 my" (t) +by'(t)+ky(t)=0. (a) Find the equation of motion for the vibrating spring with damping if m = 10 kg. b = 40 kg/sec, k=130 kg/sec². y(0)=0.3 m, and y'(0) = -0.3 m/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 0.574 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)= 10 (sin (3t) + 3 cos (3t)) e - 21 (b) The mass will first cross the equilibrium point after 1.300 seconds. (Round to three decimal places as needed.)

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 my" (t) +by'(t)+ky(t)=0. (a) Find the equation of motion for the vibrating spring with damping if m = 10 kg. b = 40 kg/sec, k=130 kg/sec². y(0)=0.3 m, and y'(0) = -0.3 m/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 0.574 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)= 10 (sin (3t) + 3 cos (3t)) e - 21 (b) The mass will first cross the equilibrium point after 1.300 seconds. (Round to three decimal places as needed.)