Question

The maximum velocity of a simple harmonic motion represented by
$y=3\sin \left(100t+\frac{\pi }{6}\right)m$ is given by:

• A. 300 m/s
• B. $\frac{\text{3}}{\text{6}}\text{m/s}$
• C. 100 m/s
• D. $\frac{\pi }{\text{6}}\text{m/s}$

Answer 1

Answer: (A)

Key Idea : Equating the given equation with general equation of $SHM$. The given equation is written as
$y=3\sin \left(100t+\frac{\pi }{6}\right)$ ....(i)
The general equation of simple harmonic motion is written as
$y=a\sin (\omega t+\varphi )$ ....(ii)
Equating Eqs. (i) and (ii), we get
$a=3,\omega =100$
Maximum velocity, $v=a\omega$
$=3\times 100$
$=300m/s$