The minimum phase difference between the two simple harmonic oscillations
`x_(1)=(1//2)sinomegat+(sqrt(3)//2)cosomegat and`
`x_(2)=(sqrt(3)//2)sinomegat+(1//2)cosomegat` is

Options

A. `pi//6`
B. `pi//3`
C. `pi//4`
D. `pi//2`

Answer

A

Explanation

`phi_(1)=tan^(-1)(B//A)=tan^(-1)((sqrt(3)/(2))/((1)/(2)))=tan^(-1)(sqrt(3))=(pi)/(3)`
`phi_(2)=tan^(-1)(B//A)=tan^(-1)(((1)/(2))/((sqrt(3))/(2)))=tan^(-1)((1)/(sqrt(3)))=(pi)/(6)`
`deltaphi=phi_(1)-phi_(2)=(pi)/(3)-(pi)/(6)=(pi)/(6)`