Two simple harmonic motion are represented by equations
`y_(1) = 4 sin (10 t + phi) rArr y_(2) = 5 cos 10t`
What is the phase difference between their velocities ?

Options

A. `pi//s`
B. `theta+pi//2`
C. `theta-(pi)/(2)`
D. `theta`

Answer

C

Explanation

For 1st particle , `y_(1)=4sin(10t+theta)`
velocity `upsilon_(1)=(dy_(1))/(dt)`
`=4xx10cos(10t+theta)=40cos(10t+theta)`
For 2nd particle,
`y_(2)=5cos(10t)=5sin(10t+(pi)/(2))`
velcoity `upsilon_(2)=(dy_(2))/(dt)=5xx10cos(10t+(pi)/(2))`
`=50cos(10t+(pi)/(2))`
Phase difference between velocities
`=(10t+theta)-(10t+(pi)/(2))=theta-(pi)/(2)`