Two particles are executing S.H.M. according to the equations
`x_(1)=6sin(10pit+pi//3)andx_(2)=5cos(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

A

Explanation

`x_(1)=6sin(10pit+(pi)/(3))`
`x_(2)=5cos(8pit+(pi)/(4))`
`=5sin(8pit+(pi)/(2)=(pi)/(4))`
`deltaphi=phi_(1)-phi_(2)`
`=(10pit+(pi)/(3))-(8pit+(pi)/(2)+(pi)/(4))`
`=2pit+(pi)/(3)-((pi)/(2)+(pi)/(4))`
`=2pixx0.5+(pi)/(3)-[(2pi+pi)/(4)]`
`=(pi+(pi)/(3))-(3pi)/(4)=((3pi+pi)/(3))-((3pi)/(4))`
`=(4pi)/(3)(3pi)/(4)=(16pi-9pi)/(12)`
`=(17)/(12)pi`