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Two simple harmonic motions are represen...

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

A

`1:1`

B

`1:2`

C

`2:1`

D

`1:sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
C
`y_(1)=5(sin2pit+sqrt(3)cos2pit)` `[becausey_(1)=rsin(2pit+phi)] and r=sqrt(a^(2)+beta^(2))`
`=5sqrt(1^(2)+(sqrt3)^(2))sin(2pit+phi)=10sin(2pit+phi)`
`y_(2)=5sin(2pit+(pi)/(4)),(A_(1))/(A_(2))=(10)/(5)=2:1`.
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