First slide

Simple hormonic motion

Question

A particle is performing simple harmonic motion. Equation of its motion is $x = 5 \sin (4 t - \frac{π}{6}), x$ being the displacement from mean position. Velocity (in ms^-1)of the particle at the instant when its displacement is 3, will be:

Moderate

A

$\frac{2 π}{3}$
B

$\frac{5 π}{6}$
C

20
D

16

Solution

$x = 5 \sin (4 t - \frac{π}{6})$
When $x = 3 \Rightarrow \frac{3}{5} = \sin (4 t - \frac{π}{6}) \Rightarrow (4 t - \frac{π}{6}) = 37^{o} velocity = \frac{dx}{dt} = 5 \times 4 \cos (4 t - \frac{π}{6}) = 5 \times 4 \times \cos 37^{o} = 16 {ms}^{- 1}$

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