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The displacement of a particle varies with time according to the relation `y=asinomega+bcosomegat`.
A. The motion is oscillatory but not SHM.
B. The motion is SHM with amplitude `a+b`.
C. The motion is SHM with amplitude `a^(2)+b^(2)`
D. The mostion is SHM with amplitude `sqrt(a^(2)+b^(2))`.

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Correct Answer - D
Given: `x=asinomegat+bcosomegat` . . . (i)
Let `a=Acosphi` . . . (ii)
Squaring and adding (ii) and (iii), we get
`a^(2)+b^(2)=A^(2)cos^(2)phi+A^(2)sin^(2)phi=A^(2)`
Eq. (i) can be written as
`x=Acosphisinomegat+Asinphicosomegat=Asin(omegat+phi)`
It is equation of SHM with amplitude `A=sqrt(a^(2)+b^(2))`.

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