A mass at the end of a spring without any damping executes simple harmonic motion. This motion is described by the equation:
y(t) = 2cos(10t),
where y is the position of the spring from rest and t is the time.
(A) Find the maximum and minimum displacement (position) of the mass. What is the period of the oscillation, T, for this mass?
(B) Find expressions for the velocity, v(t), and the acceleration, a(t) = y''(t), of the mass. Also, determine the maximum velocity of the mass and when it occurs for 0 < t < T.
