The displacement of a harmoniv oscillatore is given by `x=alphasinomegat+betacosomegat.` What is the amplitude of the oscillation?

Explanation

Given `x=alphasinomegat+betacosomegat.`
Let `alpha=rcostheta` and `beta=rsintheta` Then,
`x=rcosthetasinomegat+rsinthetacosomegat`
`=rsin(omegat+theta)`
It is an equation of simple harmonic motion, whose amplitude is r.
From above,
`alpha^(2)+beta^(2)=r^(2)cos^(2)theta+r^(2)sin^(2)theta=r^(2)`
or `r=sqrt(alpha^(2)+beta^(2))`