A block attached to an ideal spring is oscillating on a smooth horizontal surface, executing simple harmonic motion. What is the phase difference between the restoring force exerted by the spring and the velocity of the block?

Step-by-step solution

In simple harmonic motion, the displacement of the block can be represented as x = A ( t) . The velocity of the block is the rate of change of displacement: v = dx dt = A ( t) = A ( t + 2 ) The restoring force exerted by the spring is directly proportional to the negative of displacement (Hooke's Law): F = -kx = -kA ( t) = kA ( t + ) Comparing the phase angles, the phase of velocity is ( t + 2 ) and the phase of the restoring force is ( t + ) . The phase difference between the restoring force and the velocity is: =