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 a^{2} + b^{2}.

D. The motion is S.H.M. with amplitude √ a^{2} + b^{2}.

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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