Classical Harmonic Oscillator

$x(t)=\frac{v_0}{\omega }\sin (\omega t)$

• $v_0$ is the initial velocity of the particle
• $\omega =\sqrt{\frac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass

$E=\frac{1}{2}m{v}_0^2=\frac{1}{2}k{A}^2$

• $A$ is the amplitude of the oscillation