Question

A particle is performing S.H.M with time period $T$. Find the shortest time taken by the particle to go from the mean position to an extreme position.

• A. $\frac{T}{4}$
• B. $\frac{T}{8}$
• C. $\frac{T}{2}$
• D. $\frac{T}{6}$

Answer 1

The correct option is A $\frac{T}{4}$

For a particle executing SHM starting from mean position, equation can be considered as
$x=A\sin \omega t$
At $t=0,x=0$ [mean position]
For nearest extreme position, $x=A=A\sin \omega t$
$\Rightarrow \sin \omega t=1$ or $\omega t=\frac{\pi }{2}$
$\Rightarrow \frac{2\pi t}{T}=\frac{\pi }{2}$
$\Rightarrow t=\frac{T}{4}$


Alternate solution:
For a particle executing SHM, starting from mean position, time period $=T$, which is time taken by the particle to complete one full oscillation.
One full oscillation consists of motion from mean position to extreme + extreme position to mean position + mean position to the other extreme position + from the other extreme position back to mean position.
$t+t+t+t=T$
$\Rightarrow t=\frac{T}{4}$


Therefore, minimum time taken for the particle to go from MP to EP is $\frac{T}{4}$