Question

A $\text{SHM}$ is represented by the equation $x=10\text{sin}(\pi t+\frac{\pi }{6})$ in SI units. Find the maximum velocity of particle executing $\text{SHM}$.

• A. $10\pi \text{m/s}$
• B. $\frac{10}{\pi }\text{m/s}$
• C. $\frac{2\pi }{3}\text{m/s}$
• D. $-10\pi \text{m/s}$

Answer 1

The correct option is A $10\pi \text{m/s}$

Given,
$x=10\text{sin}(\pi t+\frac{\pi }{6})$
Comparing the above equation with $x=\text{A sin}(\omega t+\varphi )$ we get
$A=10\text{m}$
$\omega =\pi \text{rad/s}$
$\varphi =\frac{\pi }{6}\text{rad}$
$\therefore V_{max}=A\omega =10\pi \text{m/s}$
Hence, option (A) is correct.