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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

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12 m/s

8 m/s

17 m/s

13 m/s

answer is B.

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Detailed 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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