Question

A simple harmonic motion has an amplitude a and time period t. the minimum time required by it to travel from x=A to x=A/2

Answer 1

Since the particle starts from x=A, the equation of motion can be written as

x=Acos\omega t

Hence forx=A/2,

A/2=Acos\omega t\implies \omega t=\dfrac{\pi}{3}

\implies t=\dfrac{\pi}{3\omega}

SinceT=\dfrac{2\pi}{\omega},

t=T/6