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If two simple harmonic motions are given...

If two simple harmonic motions are given as
`x_(1)=Asin omegat andx_(2)=(A//2)sinomegat+(A//2)cosomegat`, then the ratio of their amplitudes is

A

1

B

2

C

`1//sqrt(2)`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`A_(1)=A`
`R=sqrt(A_(1)^(2)+A_(2)^(2))`
`=sqrt((A^(2))/(4)+(A^(2))/(4))=sqrt((2A^(2))/(4))=(A)/(sqrt(2))`
`(A_(1))/(R)=(A)/((A)/(sqrt(2)))=(sqrt(2))/(1)`
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