Physics Course/Oscillation

Oscillation

Oscillation refers to any Periodic Motion moving at a distance about the equilibrium position and repeat itself over and over for a period of time . Example The Oscillation up and down of a Spring , The Oscillation side by side of a Spring. The Oscillation swinging side by side of a pendulum

Spring's Oscillation

Up and down Oscillation

When apply a force on an object of mass attach to a spring . The spring will move a distance y above and below the equilibrium point and this movement keeps on repeating itself for a period of time . The movement up and down of spring for a period of time is called Oscillation

Any force acting on an object can be expressed in a differential equation

$F=m\frac{d^{2}y}{d{t}^2}$

Equilibrium is reached when

F = - F_y

$F=m\frac{d^{2}y}{d{t}^2}=-ky$

$F=\frac{d^{2}y}{d{t}^2}+\frac{k}{m}y=0$

$s^2+\frac{k}{m}s=0$

$s=\pm j\sqrt{\frac{k}{m}}t=\pm j\omega t=e^j\omega t+e^{-}j\omega t$

$y=ASin\omega t$

Side by Side Oscillation of Spring

When apply a force on an object of mass attach to a spring . The spring will move a distance x above and below the equilibrium point and this movement keeps on repeating itself for a period of time . The movement up and down of spring for a period of time is called Oscillation

Any force acting on an object can be expressed in a differential equation

$F=m\frac{d^{2}x}{d{t}^2}$

Equilibrium is reached when

F = - F_x

$F=m\frac{d^{2}x}{d{t}^2}=-kx$

$F=\frac{d^{2}x}{d{t}^2}+\frac{k}{m}x=0$

$s^2+\frac{k}{m}s=0$

$s=\pm j\sqrt{\frac{k}{m}}t=\pm j\omega t=e^j\omega t+e^{-}j\omega t$

$y=ASin\omega t$

Swinging Oscillation from side to side of Pendulum

When there is a force acting on a pendulum. The pendulum will swing from side to side for a certain period of time. This type of movement is called oscillation

$mg=-ly$

$y=\frac{mg}{l}=vt$

$t=\frac{mg}{lv}$ ||

Summary

1. Oscillation is a periodic motion.
2. Oscillation can be thought as a Sinusoidal Wave.
3. Oscillation can be expressed by a mathematic 2nd order differential equation

Oscillation	Picture	Force	Acceleration	Distance travel	Time Travelled
/Spring Oscillation/	When there is a force acting on a spring . The spring goes into an up and down motion for a certain period of time . This type of movement is called oscillation	$ma=-ky$ $m\frac{d^{2}y}{d{t}^2}=-ky$ $m\frac{d^{2}y}{d{t}^2}+ky=0$ $s=\pm j\sqrt{\frac{k}{m}}$ $y=e^{j\sqrt{\frac{k}{m}}t}+e^{-j\sqrt{\frac{k}{m}}t}$ $y=y_m\cos \left(\sqrt{\frac{k}{m}}t\right)$	$a=\frac{k}{m}y$	$y=\frac{ma}{k}=a{t}^2$	$t=\pm \sqrt{\frac{k}{m}}$
/Pendulum Oscillation/	When there is a force acting on a pendulum. The pendulum will swing from side to side for a certain period of time . This type of movement is called oscillation.	$mg=-ly$		$y=\frac{mg}{l}=vt$	$t=\frac{mg}{lv}$