As time ` t = 0` one particle is at maximum position amplitude and the other is at half at the position amplitude Their amplitude and time period `T` are same if they are appoatules find the take by which they cross each other

Options

A. `(T)/(6)`
B. `(T)/(12)`
C. `(T)/(16)`
D. `(T)/(24)`

Answer

B

Explanation

`x_(1) = A cos omega t`(at `t = 0, x_(1) = A`)
`x_(2) = A sin"(omega t + (pi)/(6))` (at `t = 0, x_(1) = A`) For `x_(1) = x_(2)`
`cos omega t= sin(omega t +pi//6)`
`cos omega t( 1 - sin(pi)/(6)) = sin omega t cos (pi)/(6)`
`tan omega t = ((1- sin pi //6))/(cos pi//6) = (1)/(sqrt(3))`
`omega t = ((2pi)/(T)) t = (pi)/(6)`
will given `t = (pi)/(12)`