# 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

$F=m{\frac {d^{2}y}{dt^{2}}}$ Equilibrium is reached when

F = - Fy
$F=m{\frac {d^{2}y}{dt^{2}}}=-ky$ $F={\frac {d^{2}y}{dt^{2}}}+{\frac {k}{m}}y=0$ $s^{2}+{\frac {k}{m}}s=0$ $s=\pm j{\sqrt {\frac {k}{m}}}t=\pm j\omega t=e^{j}\omega t+e^{-}j\omega t$ $y=ASin\omega t$ ### 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

$F=m{\frac {d^{2}x}{dt^{2}}}$ Equilibrium is reached when

F = - Fx
$F=m{\frac {d^{2}x}{dt^{2}}}=-kx$ $F={\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0$ $s^{2}+{\frac {k}{m}}s=0$ $s=\pm j{\sqrt {\frac {k}{m}}}t=\pm j\omega t=e^{j}\omega t+e^{-}j\omega t$ $y=ASin\omega t$ ### 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 $ma=-ky$ $m{\frac {d^{2}y}{dt^{2}}}=-ky$ $m{\frac {d^{2}y}{dt^{2}}}+ky=0$ $s=\pm j{\sqrt {\frac {k}{m}}}$ $y=e^{j{\sqrt {\frac {k}{m}}}t}+e^{-j{\sqrt {\frac {k}{m}}}t}$ $y=y_{m}\cos \left({\sqrt {\frac {k}{m}}}t\right)$ $a={\frac {k}{m}}y$ $y={\frac {ma}{k}}=at^{2}$ $t=\pm {\sqrt {\frac {k}{m}}}$ 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.

$mg=-ly$ $y={\frac {mg}{l}}=vt$ $t={\frac {mg}{lv}}$ 