Motion of Cart attached to Wall by Spring with no Damping

Problem Definition
Suppose the damping force $c$ is zero.

Then the motion of $C$ can be described by the second order ODE:
 * $m \dfrac {\d^2 \mathbf x} {\d t^2} = -k \mathbf x = 0$

Proof
From Motion of Cart attached to Wall by Spring under Damping:


 * $\dfrac {\d^2 \mathbf x} {\d t^2} + \dfrac c m \dfrac {\d \mathbf x} {\d t} + \dfrac k m \mathbf x = 0$

The result follows by setting $c = 0$.