A simple harmonic motion is represented as `x=Asinomegat+Bcosomegat`. Find the amplitude and initial phase.

Explanation

`x=Asinomegat+Bcosomegat`
= `sqrt(A^(2)+B^(2))" "[A/sqrt(A^(2)+B^(2))sinomegat+B/sqrt(A^(2)+B^(2))cosomegat]`
= `sqrt(A^(2)+B^(2))" "[costhetasinomegat+sinthetacosomegat]`
= `sqrt(A^(2)+B^(2))sin(omegat+theta)`
Comparing with the general equation `x=Asin(omegat+phi)` of SHM, we get,

amplitude = `sqrt(A^(2)+B^(2))`,
initial phase = `theta=tan^(-1)(B/A)`.