First slide

Simple hormonic motion

Question

A particle executes simple harmonic motion according to the displacement equation $y = 10 \cos (2 πt + \frac{π}{6}) cm;$ , where t is in seconds. The velocity of the particle at $t = \frac{1}{6}$ seconds will be:

Moderate

A

-6.28 ${ms}^{- 1}$
B

$- 0.628 {ms}^{- 1}$
C

$0.628 {ms}^{- 1}$
D

$6.28 {ms}^{- 1}$

Solution

Velocity v = $\frac{dy}{dt} = \frac{d}{dt} [10 \cos (2 πt + \frac{π}{6})]$
$= - 20 π \sin (2 πt + \frac{π}{6}) {cms}^{- 1}$
$v (\frac{1}{6}) = - 20 (3.14) \sin (\frac{π}{3} + \frac{π}{6}) {cms}^{- 1}$
= 62.8 $cm s^{- 1}$ (numerically) [Using sin $\frac{π}{2} = 1$ ]
= 0.628 ${ms}^{- 1}$

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