Physics Course/Periodic Motion

Periodic Motion

Periodic motion refers to any motion moving at a distance above and below the equilibrium position and this motion keeps repeat itself over a period of time. This type of motion is also called Oscillation .

Examples

1. The moving up and down of a spring
2. The swinging side by side of a pendulum

Analysis

The moving up and down of a spring

When apply a force on an object of mass m attach to a spring , the spring will move a distance y above and below the equilibrium point

The force acts on the object is

F = m a

The Restoring Force of spring is given by Hook's law as

Fs = - k y

When The Net Force on the system is 0 then there is no movement

F - Fs = 0
m a = - k y
y = ${\displaystyle {\frac {ma}{k}}}$
a = - ${\displaystyle {\frac {k}{m}}y}$
v t = ${\displaystyle {\frac {k}{m}}y}$
${\displaystyle t={\frac {k}{m}}{\frac {y}{v}}}$