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.