Question

A particle executes S.H.M. from extreme position and covers a distance equal to half of its amplitude in $1s$. Determine the time period of motion.

• A. $10s$
• B. $16s$
• C. $6s$
• D. $12s$

Answer 1

The correct option is C $6s$

We know that the distance covered by a particle is SHM is given by

$x=Acos\omega t$

Now in this case distance covered is half the amplitude so, $x=\frac{A}{2}$ and $t=1$ sec .

Therefore , $\frac{A}{2}=Acos\omega \times 1$

Or, $\frac{1}{2}=cos\omega$

Or, $cos\frac{\pi }{3}=cos\omega$

Or, $\omega =\frac{\pi }{3}$

Now time period $T=\frac{2\pi }{\omega }$

Or, $T=\frac{2\pi }{\frac{\pi }{3}}$

Or, $T=6$ secs