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Two simple harmonic motions are represen...

Two simple harmonic motions are represented by `y_(1)=5[sin2pit+sqrt(3)cos2pit]` and `y_(2)=5sin(2pit+(pi)/(4))` The ratio of their amplitudes is

A

`1:3`

B

`sqrt(3):1`

C

`1:1`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`y_(1)=5[sin 2pi t+sqrt(3)cos 2pi t]`
`=10[(1)/(2)sin 2pi t+(sqrt(3))/(2)cos 2pi t]`
`=10[cos""(pi)/(3)sin2pi t+sin""(pi)/(3)cos 2pi t]`
`y_(1)=10 sin(2pi t+(pi)/(3))`
`y_(2)=5sin(2pi t+(pi)/(4))`
So ratio of amplitude of `y_(1)` and `y_(2)` is `(10)/(5)=(2)/(1)`
So correct choice is (d).
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