Question

Derive the equation of motion of a simple harmonic motion and obtain the expression for its velocity time period and frequency

Answer 1

$\ddot x+\frac km x=0,$

$\omega^2={\frac km},$

$\ddot x+\omega^2 x=0,$

$\omega=\sqrt{\frac km},$

$T=\frac{2\pi}{\omega}=2\pi\sqrt{\frac mk}.$