The diplacement of a particle executing simple harmonic motion is given by `y=A_(0)+A sin omegat+B cos omegat`. 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`
`or (y-A_(0))=Asinomegat+Bcosomegat`
or `y.=Asinomegat+Bcosomegat=Acos((pi)/(2)-omegat)+Bcosomegat`
Amplitude `=sqrt(A^(2)+B^(2)+2ABcos.(pi)/(2))[because phi=(pi)/(2)]`
`=sqrt(A^(2)+B^(2))`