 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiate the sum of <kinetic energy> and <potential energy> using the <dot product> product rule:
$$
\frac{dE}{dt}=m\dot{\mathbf r}\cdot\ddot{\mathbf r}
+k\mathbf r\cdot\dot{\mathbf r}
=\dot{\mathbf r}\cdot(m\ddot{\mathbf r}+k\mathbf r)=0.
$$
The equations of motion make the bracket zero. Hence the <mechanical energy> is \b[constant in <time>]. The central <restoring force> can exchange kinetic and <potential energy> but supplies no change in their sum.

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