The displacement equation of a particle ...

The displacement equation of a particle is `x=3 sin 2t+4cos2t`. The amplitude and maximum velocity will be respectively

A

5,10

B

3,2

C

4,2

D

3,4

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The correct Answer is:

A

(a) `x=3 "sin"2t+4"cos"2t.`From given equation

`a_(1)=3,a_(2)=4` and `phi=(pi)/(2)`
`therefore a=sqrt(a_(1)^(2)+a_(2)^(2))=sqrt(3^(2)+4^(2))=5`
`impliesv_("max")=alphaomega=5xx2=10`

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