What is the minimum phase difference between two S.H.M.s given by `x_(2)= "sin" omega t + "cos" omegat t " and " x_(1)=(1)/(2) "sin" omega t + (sqrt(3))/(2) "cos" omega t`

Options

A. `(pi)/(4)`
B. `(pi)/(12)`
C. `(pi)/(3)`
D. `-(pi)/(4)`

Answer

B

Explanation

`x_(1)=(1)/(2) "sin" omega t +(sqrt(3))/(2) "cos" omega t`
`= "cos" (pi)/(3) "sin" omega t+ "sin" (pi)/(3) "cos" omega t= "sin" (omega t+(pi)/(3))`
`x_(2)= "sin" omega t+ "cos" omega t`
`=sqrt(2)[(1)/(sqrt(2)) "sin" omega t + (1)/(sqrt(2)) "cos" omega t]`
`=sqrt(2)["cos" (pi)/(4) "sin" omega t + "sin" (pi)/(4) "cos" omega t]`
`=sqrt(2) "sin" (omega t+(pi)/(4))`
`therefore " Phase difference " =(pi)/(3)-(pi)/(4)=(pi)/(12)`