Question

A simple pendulum performs simple harmonic motion about $x=0$ with an amplitude ${}^{\prime }{a}^{\prime }$ and time period ${}^{\prime }{T}^{\prime }$. The speed of the pendulum at $x=\frac{a}{2}$ will be:

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

Answer 1

The correct option is C $\frac{\pi a\sqrt{3}}{T}$

As simple pendulum performs simple harmonic motion.
$\therefore velocity,v=\omega \sqrt{a^2-x^2}$
At, $x=\frac{a}{2}$
$v=\frac{2\pi }{T}\sqrt{a^2-{\left(\frac{a}{2}\right)}^2}=\frac{2\pi }{T}\frac{\sqrt{3a^2}}{2}=\frac{\pi a\sqrt{3}}{T}$