Simple Harmonic Oscillator
#Physics
Undamped
$\displaystyle \ddot{x}+\omega^{2}x=0$
Solutions
- $\displaystyle x(t)=C_{1}e^{i\omega t}+C_{2}e^{-i\omega t}$
- $\displaystyle x(t)=C_{1}\cos(\omega t)+C_{2}\sin(\omega t)$
- $\displaystyle x(t)=A\cos(\omega t+phi)$