# Physics Course/Oscillation

## OscillationEdit

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 OscillationEdit

### Up and down OscillationEdit

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

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

Equilibrium is reached when

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

### Side by Side Oscillation of SpringEdit

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

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

Equilibrium is reached when

F = - Fx
${\displaystyle F=m{\frac {d^{2}x}{dt^{2}}}=-kx}$
${\displaystyle F={\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0}$
${\displaystyle s^{2}+{\frac {k}{m}}s=0}$
${\displaystyle s=\pm j{\sqrt {\frac {k}{m}}}t=\pm j\omega t=e^{j}\omega t+e^{-}j\omega t}$
${\displaystyle y=ASin\omega t}$

### Swinging Oscillation from site to site of PendulumEdit

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

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

## SummaryEdit

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

${\displaystyle ma=-ky}$

${\displaystyle m{\frac {d^{2}y}{dt^{2}}}=-ky}$

${\displaystyle m{\frac {d^{2}y}{dt^{2}}}+ky=0}$
${\displaystyle s=\pm j{\sqrt {\frac {k}{m}}}}$
${\displaystyle y=e^{j{\sqrt {\frac {k}{m}}}t}+e^{-j{\sqrt {\frac {k}{m}}}t}}$
${\displaystyle y=y_{m}\cos \left({\sqrt {\frac {k}{m}}}t\right)}$

${\displaystyle a={\frac {k}{m}}y}$  ${\displaystyle y={\frac {ma}{k}}=at^{2}}$  ${\displaystyle t=\pm {\sqrt {\frac {k}{m}}}}$
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
${\displaystyle mg=-ly}$  ${\displaystyle y={\frac {mg}{l}}=vt}$  ${\displaystyle t={\frac {mg}{lv}}}$