Q. 64.5( 2 Votes )

The displacement of a particle varies with time according to the relation

y = a sin ωt + b cos ωt.

A. The motion is oscillatory but not S.H.M.

B. The motion is S.H.M. with amplitude a + b.

C. The motion is S.H.M. with amplitude a2 + b2.

D. The motion is S.H.M. with amplitude √ a2 + b2.

Answer :

Consider the equation,



now, let and


now putting the above in the given equation,




Now using the identity


Thus, we get,


Thus, the motion is SHM with amplitude


the option (d) is correct.

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