# Physics Course/Oscillation/Oscillation Side by Side

## Oscillation Side by Side

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

### 1

The force acts on the object to pull the object down

F = m a

The Restoring Force of spring to push the object up can be calculated by Hook's Law

Fs = - k y

The oscillation stops when the two forces are equal or the net force on object is zero

m a = - k y
y = ${\frac {ma}{k}}$ a = - ${\frac {k}{m}}y$ $t={\frac {k}{m}}{\frac {y}{v}}$ ### 2

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

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

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