Question

A particle has simple harmonic motion. The equa-tion of its motion is $x=5\sin (4t-\pi /6)$, where $x$ is its displacement. If the displacement of the particle is $3units$, then its velocity is

• A. $2\pi /3$ units
• B. $5\pi /6$ units
• C. $20$ units
• D. $16$ units

Answer 1

Answer: (C)

$20$ units

From the given equation,

The amplitude of the wave is $a=5$

and the angular velocity of the wave is $\omega =4$

The velocity of the wave can be obtained as:

$\therefore v=\omega \sqrt{a^2-y^2}$

$=4\sqrt{(5{)}^2-(3{)}^2}=16units$