Two particle `P` and `Q` describe `S.H.M.` of same amplitude a same frequency `f` along the same straight line .The maximum distance between the two particles is `asqrt(2)` The phase difference between the two particle is

Options

A. zero
B. `(pi)/(2)`
C. `(pi)/(6)`
D. `(pi)/(3)`

Answer

B

Explanation

`y_1=asinomegat` and `y_2=sin(omegat+phi)`
`y_2-y_1=asqrt2=asin(omegat+phi)-asinomegat`
or `sqrt(2)a=2acos((omegat+phi+omegat)/(2))=sin((omegat+phi+omega)/(2))`
`=2acos(omegat+(phi)/(2))sin(phi)/(sqrt2)`
For maximum value `cos(omegat+phi)=1`, therefore
`2sin(phi)/(2)=sqrt2impliessin(phi)/(2)=(1)/(sqrt2)`
or `(phi)/(2)=(pi)/(4)` or `phi=(pi)/(2)`