Q. The maximum velocity of a simple harmonic motion represented by $y = 3\ sin(100t + \frac{\pi}{6})m$ is given by
A) $300\ ms^{- 1}$
B) $\frac{3\pi}{6}\ ms^{- 1}$
C) $100\ ms^{- 1}$
D) $\frac{\pi}{6}\ ms^{- 1}$
Explanation
(a) 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
$y = a\sin{(\omega t + \varnothing)}$ …(ii)
Equating Eqs. (i) and (ii), we get
$a = 3,\ \omega = 100$
Maximum velocity, $v = a\omega$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3 \times 100 = 300\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.