Derive the equation of motion of a simple harmonic motion and obtain the expression for its velocity time period and frequency
x¨+kmx=0,\ddot x+\frac km x=0,x¨+mkx=0,
ω2=km,\omega^2={\frac km},ω2=mk,
x¨+ω2x=0,\ddot x+\omega^2 x=0,x¨+ω2x=0,
ω=km,\omega=\sqrt{\frac km},ω=mk,
T=2πω=2πmk.T=\frac{2\pi}{\omega}=2\pi\sqrt{\frac mk}.T=ω2π=2πkm.
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