Harmonic Oscillator

A solution to Newton’s 2nd law where the Force is given by Hooke`s law, $F(x)=-kx,k\in {\mathbb{R}}^{+}$. The relevant Equation of motion is $m\ddot{x}+kx=0$, and the general solution is $x(t)=a\cos (\omega t)+b\sin (\omega t)$