Question

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

300 m/s

Answer 2

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