Two simple harmonic motions are represented by the equations `y_(1)=0.1sin(100pit+pi/3)andy_(2)=0.1cospit`. What is the initial phase difference of the velocity of the first particle with respect to the second?

Explanation

`y_(1)=0.1sin(100pit+pi/3)`,
Velocity, `v_(1)=(dy_(1))/(dt)=100pixx0.1cos(100pit+pi/3)`
= `10picos(100pit+pi/3)`
Phase, `phi_(1)=pi/3` at time t = 0
`y_(2)=0.1cospit`
Velocity, `v_(2)=(dy_(2))/(dt)=-0.1pisinpit=0.1picos(pit+pi/2)`
Phase, `phi_(2)=pi/2` at time t = 0
`therefore` Phase difference = `theta_(1)-theta_(2)=pi/3-pi/2=-pi/6`