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Problem 3. (10 points) A 10 kg mass is placed on a spring and stretched 50cm to equilibrium. The mass is then stretched 20cm below equilibrium and given an upward velocity of 1m/s. The motion is then damped by 2"2 and subjected to an additional force of 3 sin(t) N. For the following problem, use g = 9.8m (a) Use Hooke's law to determine the spring constant, k. (b) What is y(0)? (c) What is y'(0)? (d) Set up the initial value problem which describes the displacement of the block from equilibrium in meters at time t > 0. Solution