A coin of mass m sits on top of a spring that oscillates vertically, up and down, with small amplitude (follows Hooke's law). [m = 0.01 kg; g = 9.82 m/s2] Derive an equation that describes the motion of the coin in the vertical direction its function of time, y(t), if one assumes the coin stays in contact with the spring at all times. You may assume the motion of the spring-coin system is oscillatory. The amplitude of the oscillation is 1.2 cm. What is the maximum frequency f = omega/2pi that assures the coin remains in contact with the spring throughout?