Question

A particle performs linear S.H.M. of period 4 seconds and amplitude 4 cm. Find the time taken by it to travel a distance of 1 cm from the positive extreme position

Answer 1

Given that,

Time period = 4 sec

Amplitude = 4 cm

Distance = 1 cm

We need to calculate the angular velocity

Using formula of angular velocity

$\omega=\dfrac{2\pi}{T}$

Where, T = time period

Put the value into the formula

$\omega=\dfrac{2\pi}{4}$

$\omega=\dfrac{\pi}{2}$

We need to calculate the time taken

Using phase diagram

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

$t=\dfrac{\pi}{3}\times\dfrac{2}{\pi}$

$t=\dfrac{2}{3}\ s$

Hence, The time taken is $\dfrac{2}{3}\ s$