The displacement of a particle executing simple harmonic motion is given by
`y=A_(0)+Asinomegat+Bcosomegat`
Then the amplitude of its oscillation is given by :

Options

A. `A+B`
B. `A_(0)+sqrt(A^(2)+B^(2))`
C. `sqrt(A^(2)+B^(2))`
D. `sqrt(A_(0)^(2)+(A+B)^(2))`

Answer

C

Explanation

`y=A_(0)+Asinomegat+Bcosomegat`
Hence, 2 SHM.s are super imposed with phase difference of `pi/2`
Amplitude `=sqrt(A^(2)+B^(2)+2ABcosDeltaphi)" "[because Deltaphi=(pi)/(2)]`
`=sqrt(A^(2)+B^(2))`.