Simple Harmonic Oscillator

#Physics

Undamped

$\displaystyle \ddot{x}+\omega^{2}x=0$

Solutions

  • $\displaystyle x(t)=C_{1}e^{i\omega t}+C_{2}e^{-i\omega t}$
  • $\displaystyle x(t)=C_{1}\cos(\omega t)+C_{2}\sin(\omega t)$
  • $\displaystyle x(t)=A\cos(\omega t+phi)$

Damped

Underdamped

Overdamped

Critically Damped