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Equations y(1) =A sinomegat and y(2) = ...

Equations ` y_(1) =A sinomegat and y_(2) = A/2 sin omegat + A/2 cos omega t ` represent S.H.M. The ratio of the amplitudes of the two motions is

A

0.5

B

`sqrt(2)`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Given , `y_(1) =A "sin"omegat`
and `y_(2)=(A)/(2)"sin"omegat+(A)/(2)"cos"omegat`
or `y_(2)=(A)/(2)("sin"omegat+"cos"omegat)`
`=(A)/(2)sqrt(2)["sin"(omegat+45^(@))]=(A)/(sqrt(2))"sin"(omegat+45^(@))`
`therefore` The ratio of amplitude of two motions
`(A_(1))/(A_(2))=(A)/(A//sqrt(2))=sqrt(2)`
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