Write down the equation of time period for linear harmonic oscillator ?

Explanation

From Newton.s second law, we can write the equation for the particle executing simple harmonic motion
`m(d^(2)x)/(dt^(2))=-kx" "...(1)`
`(d^(2)x)/(dt^(2))=-(k)/(m)x" "...(2)`
Comparing the equation with simple harmonic motion equation, we get
`omega^(2)=(k)/(m)" "...(3)`
which means the angular frequency or natural frequency of the oscillator is
`omega=sqrt((k)/(m))" rad "s^(-1)" " ...(4)`
The frequency of the oscillation is
`f=(omega)/(2pi)=(1)/(2pi)sqrt((k)/(m))" Hertz "...(5)`
and the time period of the oscillation is
`T=(1)/(f)=2pisqrt((m)/(k))" seconds "...(6)`