6) 18 pts] Wile E. Coyote has attached an anvil with a mass of 35 kg to a spring with a natural length of 1.5 meters. At equilibrium, the mass stretches the spring to a total length of 4 meters. He attaches the spring to a cantilevered beam at the edge of a cliff, so that when at equilibrium, the mass is hanging 3 meters below the top of the cliff. He scouts for his arch enemy, the Road Runner, and when he sees him heading his directions, raise the mass as high as he can (to a grand height of 1.5 meters above the top of the cliff), and hurls the anvil down at the Road Runner with an initial velocity of 14 m/s. Air resistance provides a damping force that is equal to V2 times the instantaneous velocity. Take displacement that stretches the spring to be positive. Use 9.8 m/s2 for g. (a) Set up the model (a rate of change equation) for the motion of the anvil at time t, x(t). Include necessary initial conditions. Do NOT take the time to fully solve the problem. (b) is the system overdamped, critically damped, or underdamped? 6) 18 pts] Wile E. Coyote has attached an anvil with a mass of 35 kg to a spring with a natural length of 1.5 meters. At equilibrium, the mass stretches the spring to a total length of 4 meters. He attaches the spring to a cantilevered beam at the edge of a cliff, so that when at equilibrium, the mass is hanging 3 meters below the top of the cliff. He scouts for his arch enemy, the Road Runner, and when he sees him heading his directions, raise the mass as high as he can (to a grand height of 1.5 meters above the top of the cliff), and hurls the anvil down at the Road Runner with an initial velocity of 14 m/s. Air resistance provides a damping force that is equal to V2 times the instantaneous velocity. Take displacement that stretches the spring to be positive. Use 9.8 m/s2 for g. (a) Set up the model (a rate of change equation) for the motion of the anvil at time t, x(t). Include necessary initial conditions. Do NOT take the time to fully solve the problem. (b) is the system overdamped, critically damped, or underdamped