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When two displacements represented by y(...

When two displacements represented by `y_(1)=asin(omegat)andy_(2)=bcos(omegat)` are superimposed, the motion is

A

not a simple harmonic

B

simple harmonic with amplitude `a/b`

C

simple harmonic with amplitude `sqrt(a^(2)+b^(2))`

D

simple harmonic with amplitude `((a+b))/2`

Text Solution

Verified by Experts

The correct Answer is:
C
y = `y_(1)+y_(2)=asinomegat+bcosomegat`
`sqrt(a^(2)+b^(2))(sinomegat*a/(sqrt(a^(2)+b^(2)))+cosomegat*b/(sqrt(a^(2)+b^(2))))`
= `sqrt(a^(2)+b^(2))(sinomegatcostheta+cosomegatsintheta)`
= `sqrt(a^(2)+b^(2))(sinomegat+theta)`
Hence, this is a simple harmonic motion, whose amplitude = `sqrt(a^(2)+b^(2))`
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