First slide

Simple hormonic motion

Question

A particle is executing simple harmonic motion according to the equation $x = (5 \cos 100 t + 12 \sin 100 t)$ cm where t is time in second. Then maximum velocity of the particle is

Easy

A

12 m/s
B

13 m/s
C

17 m/s
D

8 m/s

Solution

$x = (5 \cos 100 t + 12 \sin 100 t) c m$
Amplitude $= \sqrt{5^{2} + 12^{2}}$
$\Rightarrow A = 13 c m;$ Angular frequency $ω = 100 r a d / s$
$∴ V_{\max} = ω A = 100 \times (13 \times 10^{- 2}) m / s = 13 m / s$

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