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The motion of a particle is given by x=A...

The motion of a particle is given by `x=A sin omegat+Bcos omegat`. The motion of the particle is

A

not simple harmonic

B

simple harmonic with amplitude A+B

C

simple harmonic with amplitude `((A+B))/(2)`

D

simple harmonic with amplitude `sqrt(A^(2)+B^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
(d)`x=A "sin" omegat`

`=sqrt(A^(2)+B^(2)) ((A)/(sqrt(A^(2)+B^(2)))"sin "omegat+(B)/(sqrt(A^(2)+B^(2)))"cos "omegat)=sqrt(A^(2)+B^(2))" sin"(omegat+phi)`
where, tan `phi=(B)/(A)`
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