Two simple harmonic motions are represented by the equations y1=0.1sin(100πt+π3) and y2=0.1cosπt. The phase difference of the velocity of particle 1 with respect to velocity of particle 2 at t=0 is
y1=0.1sin(100πt+π3)
y2=0.1cosπt=0.1sin(π2+πt)=0.1sin(πt+π2)
Now, for finding velocity of particle , differentiate both equations with respect to time .
dy1dt=v1=0.1×100πcos(100πt+π3)
similarly for 2nd equation,
dy1dt=v2=0.1×πcos(πt+π2)=0.1πcos(πt+π2)
if equation x=Asin(ωt+ϕ) is given then, at t=0 phase of motion is ϕ
similarly at t=0 phas of 1st particle velocity is π3
at t=0 phase of velocity of 2nd particle is π2
now thw phase difference = phase of 1st particle at t=0 - phase of 2nd particle att=0
=π3−π2=−π6