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The displacement equation of a simple harmonic oscillator is given by `y=A sin omegat-Bcos omegat` The amplitude of the oscillator will beA. A - BB. A + BC. `sqrt(A^(2) + B^(2))`D. `(A^(2) + B^(2))`

Answer» Correct Answer - C
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))`


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