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