A block of mass �m is attached to a spring with spring constant �k and placed o

A block of mass
�m is attached to a spring with spring constant �k and placed on a frictionless horizontal surface. The block is initially at rest and is displaced a distance �x from its equilibrium position and released.
Derive the equation of motion for the block.
Solve the differential equation obtained in part 1 to find the equation of motion for �(�)x(t), where �t is time.
Determine the period of oscillation of the block-spring system in terms of �m and �k.
Sketch the graph of �(�)x(t) showing one complete cycle of oscillation.