The displacements of two linear simple harmonic oscillators are given by `x_(1)=3 "sin" (100 t+ theta) " and " x_(2)=4 "cos" (100 t)`. What is the phase difference between the velocities of these oscillators ?

Options

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

Answer

B

Explanation

`x_(1)=3 "sin" (100 t+ theta)`
`therefore v_(1)=(dx_(1))/(dt)=3xx100xx"cos" (100t + theta)`
and `x_(2)=4 "cos" (100 t)=4 "sin" (100 t+ pi //2)`
`therefore v_(2)=(dx_(2))/(dt)=4xx100xx"cos"(100 t + pi//2)`
`therefore " Phase diff". =(100 t+ theta -100t -pi//2)=(theta-pi//2)`