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The displacement of a particle varies wi...

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))`.

Text Solution

Verified by Experts

The correct Answer is:
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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Knowledge Check

  • The displacement of a particle varies with time according to the relation y=a sin omega t +b cos omega t .

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