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Question

The displacement equation of a particle is $$x = 3 \sin 2t + 4 \cos 2t $$ . The amplitude and maximum velocity will be respectively 


A
5,10
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B
3,2
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C
4,2
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D
3,4
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Solution

The correct option is A $$5,10$$

The displacement of the particle is in the form of

$$x = A\sin \omega t + B\cos \omega t$$

The amplitude is given as

$$A = \sqrt {{3^2} + {4^2}} $$

Hence the amplitude is given as$$5$$

The phase difference is of$$\frac{\pi }{2}$$

The maximum speed is given as

$${v_{\max }} = A\omega $$

$${v_{\max }} = 5 \times 2$$

Hence the maximum velocity is$$10$$


Physics

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