Question

A particle executes SHM , with amplitude & $cm$ and time period $\frac{1}{2}$ see then velocity of particle at $1=\frac{1}{16}$ sec is

• A. $32\frac{\pi }{\sqrt{2}}cm/sec$
• B. $16\sqrt{2}=cm/sec$
• C. $16\pi cm/sec$
• D. $8\pi cm/sec$

Answer 1

The correct option is A $32\frac{\pi }{\sqrt{2}}cm/sec$

$\begin{array}{c}A=8cm\\ T=\frac{1}{2}s=\frac{2\pi }{w}\\ w=4\pi \\ v=w\sqrt{A^2-x^2}\\ \therefore x=A\sin wt\\ x=A\sin \left[4\pi \times \frac{1}{6}\right]\\ =\frac{A}{\sqrt{2}}\\ v=4\pi \sqrt{A^2-\frac{A^2}{2}}=\frac{4\pi }{\sqrt{2}}.8=\frac{32}{\sqrt{2}}\pi cm/s\end{array}$