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 , ( d^(2) x)/( dt^(2)) = - k/m x `
Comparing the equation with simple harmonic motion equation ,
` a = (d^(2)y)/(dt^(2)) = - omega^(2)y " we get " omega = sqrt(k/m) rad s^(-1)` The frequency of the oscillation is
` F = omega/( 2pi) = 1/( 2pi) sqrt(k/m) " Hertz`
and the time period of the oscillation is
` T = 1/f = 2pi sqrt(m/k)` seconds