Solution
= Solution
<Hooke's law> and <Newton's second law> give $m\ddot x=-kx$, so $\omega_0=\sqrt{k/m}$. The initial conditions select the <simple harmonic motion>
$$
\boxed{x(t)=x_0\cos\omega_0t,\qquad
K(t)=\frac{kx_0^2}{2}\sin^2\omega_0t,\qquad
U(t)=\frac{kx_0^2}{2}\cos^2\omega_0t.}
$$
The <kinetic energy> and <elastic potential energy> exchange periodically while their sum $E_0=kx_0^2/2$ is constant.