The displacement equation of a simple harmonic oscillator is given by `y=A sin omegat-Bcos omegat`
The amplitude of the oscillator will be

Options

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

Answer

C

Explanation

Displacement equation
`y=A sin omegat-B cos omemgat`
Let `A=a cos theta and B=a sin theta`
So, `A^(2)+B^(2)=a^(2)`
`Rightarrow a=sqrt(A^(2)+B^(2))`
Then, `y=a cos theta sin omega t-a sin theta cos omega t`
Which is the equation of simple harmonic oscillator.
The amplitude of the oscillator
`=a=sqrt(A^(2)+B^(2))`