Oscillation

Name	Definition	Note
SIMPLE HARMONIC MOTION
Simple harmonic motion	Occurs when there is a force always act toward equilibrium point and the force is directly proportional to the displacement from equilibrium
Equation of simple harmonic motion	$a=Aw^{2} cos wt=-w^{2}x$	$v_{max}=x_{o}w$ $a_{max}=x_{o}w^{2}$
	$a=frac{d^{2}x}{dt^{2}}rightarrow frac{d^{2}x}{dt^{2}}=-w^{2}x$	$x=x_{o}cos wt$ $x=x_{o}sin wt$
	This equation has 2 solutions that tell us how x changes with time $x_{o}$ is the maximum displacement from equilibrium = amplitude
Angular frequency		$w=sqrt{frac{k}{m}}=sqrt{frac{g}{l}}$
RESONANCE
Resonance	Occur when the driving frequency is close to the natural frequency Maximum energy transferred from the driver to the oscillator The amplitude of oscillation increases rapidly/ the oscillation is amplified The amount of amplification ↓ as damping ↑ (the width of the curve ↑)
DAMPING
Damping	A resistive force that opposes the natural motion of an oscillator Energy is dissipated from the oscillation So, the amplitude of the oscillation decrease
Light damping	With air resistance, T does not change The amplitude decreases exponentially	$s=s_{o}e^{-kt}cos wt$
Heavy damping	No oscillation The object returns to equilibrium point slowly
Critical Damping	The most efficient way of removing energy from an oscillator