Problem 1: Suppose that a spring is attached to a ceiling. When a mass of 5 kilograms is attached to the free end of the spring and the spring-mass system is equilibrated, the spring elongates by 2.45 meters. The mass is then released from the new equilibrium position with an upward velocity of 1 m/s. Assuming that there is no friction in the system and that an additional external downward force F = 30 sin t is applied to the mass, find the position of the mass at any time t > 0. HINT: You can assume that the gravitatonal acceleration is g = 9.8 m/s, then simplify the expression for k as much as possible.

Problem 1: Suppose that a spring is attached to a ceiling. When a mass of 5 kilograms is attached to the free end of the spring and the spring-mass system is equilibrated, the spring elongates by 2.45 meters. The mass is then released from the new equilibrium position with an upward velocity of 1 m/s. Assuming that there is no friction in the system and that an additional external downward force F = 30 sin t is applied to the mass, find the position of the mass at any time t > 0. HINT: You can assume that the gravitatonal acceleration is g = 9.8 m/s, then simplify the expression for k as much as possible.