First slide

Simple harmonic motion

Question

A particle has simple harmonic motion. The equation of its motion is $x = 5 \sin (4 t - \frac{π}{6})$ , where x is its displacement. If the displacement of the particle is 3 units, then its velocity is

Moderate

A

$\frac{2 π}{3}$
B

$\frac{5 π}{6}$
C

20
D

16

Solution

From the given equation, a = 5 and $ω = 4$
$∴ v = ω \sqrt{a^{2} - y^{2}} = 4 \sqrt{{(5)}^{2} - {(3)}^{2}} = 16$

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