Question

At a particular position the velocity of a particle in SHM with amplitude a is $\frac{\sqrt{3}}{2}$ that at its mean position. In this position, its displacement is:

• A. $\frac{a}{2}$
• B. $\sqrt{3}\frac{a}{2}$
• C. $a\sqrt{2}$
• D. $\sqrt{2a}$

Answer 1

The correct option is A $\frac{a}{2}$

Let the equation of SHM is $x=asin\left(\omega t\right)$,

$\therefore v=a\omega cos\left(\omega t\right)$ $\Rightarrow$ Velocity at mean position $v=a\omega$,

As given in question, $\frac{\sqrt{3}}{2}a\omega =a\omega cos\left(\omega t\right)$ $\Rightarrow cos\left(\omega t\right)=\frac{\sqrt{3}}{2}$ $\Rightarrow \omega t=\frac{\pi }{6}$

So Displacement $x=asin\left(\frac{\pi }{6}\right)=\frac{a}{2}$