Physics - SHM Question with Solution | TestHub

The equation for the displacement of a particle executing simple harmonic motion starting from the mean position is given by $x=a\sin (\omega t)$.

Given that the displacement is $x=\frac{a}{\sqrt{2}}$, we can substitute this into the equation to get:

$\frac{a}{\sqrt{2}}=a\sin (\omega t)$

$\sin (\omega t)=\frac{1}{\sqrt{2}}$

For the shortest time, we consider the smallest positive angle:

$\omega t=\frac{\pi }{4}$

Substituting $\omega =\frac{2\pi }{T}$ into the equation:

$\frac{2\pi }{T}t=\frac{\pi }{4}$

$t=\frac{T}{8}$

Answer: $T/8$