Two particles are executing S.H.M. according to the equations
`x_(1)=6sin(10pit+pi//3)andx_(2)=6cos(8pit+pi//4)`
Then the phase difference between the first and second particle at t = 0.5 s will be

Options

A. `(7pi)/(12)`
B. `(13pi)/(12)`
C. `(25pi)/(12)`
D. `(pi)/(12)`

Answer

B

Explanation

`x_(1)=6sin(10pit+(pi)/(3))`
`x_(2)=6sin(8pit+(pi)/(4))`
`deltaphi=phi_(1)-phi_(2)=(10pit+(pi)/(3))-(8pit+(pi)/(4))`
`=2pit+(pi)/(3)-(pi)/(4)`
`=2pixx0.5+(4pi-3pi)/(12)=pi+(pi)/(12)`
`=(13pi)/(12)`.