The displacement equation of a particle is
$x = [3 sin (4 t) + 4 sin (4 t)] c m$ . The amplitude and maximum speed of the particle during oscillation will be

4 c m, 2 c m s^{- 1}

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2 c m, 4 c m s^{- 1}

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10 c m, 5 c m s^{- 1}

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5 c m, 20 c m s^{- 1}

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Solution

The correct option is D $5 c m, 20 c m s^{- 1}$
Position, $x = 3 sin (4 t) + 4 cos (4 t) c m \Rightarrow x = 5 [\frac{3}{5} sin (4 t) + \frac{4}{5} cos (4 t)] \Rightarrow x = 5 [cos α sin (4 t) + sin α cos (4 t)] \Rightarrow x = 5 sin (4 t + α) c m \Rightarrow$ Amplitude, $A = 5 c m$
Also, Speed $v = \frac{d x}{d t} = 5 [4 cos (4 t + α)] \Rightarrow v_{m a x} = 20 c m s^{- 1}$

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The displacement equation of a particle is x=[3sin(4t)+4sin(4t)] cm . The amplitude and maximum speed of the particle during oscillation will be

The correct option is D 5 cm,20 cm s−1Position, x=3sin(4t)+4cos(4t) cm⇒x=5[35sin(4t)+45cos(4t)]⇒x=5[cosαsin(4t)+sinαcos(4t)]⇒x=5sin(4t+α)cm⇒ Amplitude, A=5 cm Also, Speed v=dxdt=5[4cos(4t+α)]⇒vmax=20 cm s−1

The displacement equation of a particle is
$x = [3 sin (4 t) + 4 sin (4 t)] c m$ . The amplitude and maximum speed of the particle during oscillation will be