Problem 3 Consider a block-spring system inside a box, as shown in the figure. The block is attached to the spring, which is attached to the inside wall of the box. The mass of the block is 0.2 kg. For parts (a) through (f), assume that the box does not move. Suppose you pull the block 10 cm to the right and release it. The angular frequency of the oscillations is 30 rad/s. Neglect friction between the block and the bottom of the box. (a) What is the spring constant? M (b) What will be the amplitude of the oscillations? (c) Taking to the right to be positive, at what point in the oscillation is the velocity minimum and what is its minimum value? (d) At what point in the oscillation is the acceleration minimum, and what is its minimum value? (e) What is the total energy of the spring-block system? (f) If you take t 0 to be the instant when you release the block, write an equation of motion for the oscillation, x(t) =?, identifying the values of all constants that you use. (g) Imagine now that the box, with the spring and block in it, starts moving to the left with an acceleration a=4 m/s. By how much does the equilibrium position of the block shift (relative to the box), and in what direction? Problem 4 For this problem, imagine that you are on a ship that is oscillating up and down on a rough sea. Assume for simplicity that this is simple harmonic motion (in the vertical direction) with amplitude 5 cm and frequency 2 Hz. There is a box on the floor with mass m = 1 kg. (a) Assuming the box remains in contact with the floor throughout, find the maximum and minimum values of the normal force exerted on it by the floor over an oscillation cycle. (b) How large would the amplitude of the oscillations have to become for the box to lose contact with the floor, assuming the frequency remains constant? (Hint: what is the value of the normal force at the