Physics Course/Oscillation/Oscillation Up and Down

The Oscillation up and down of a Spring ]]

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

Fs = - Fa
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 differential equation

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

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