Find the time taken by the particle in going from ` x = (A)/2` to `x=A`
Hint `: t_(1) =` Time taken to go from `x=0` to `x =A `
`t_(2) = ` Time taken to go from `x=0` to`x= (A)/(2)`
Required time `= t_(1) - t_(2)`

Options

A. `T_(1) = T_(2)`
B. `T_(1) gt T_(2)`
C. `T_(1) lt T_(2)`
D. `T_(1) = (T_(2))/(2)`

Answer

C

Explanation

Time to go from O to `(A)/(2),(A)/(2)=A sin((2piT_(1))/(T))`
`therefore" "(1)/(2)="sin"(pi)/(6)=sin((2piT_(1))/(T))`
`therefore" "(2 pi T_(1))/(T)=(pi)/(6)`
`therefore" "T_(1)=(T)/(12)`
Time to go form O to A is `(T)/(4)`
`therefore` Time to go from `(A)/(2)` to `A = (T)/(4)-(T)/(12)=(T)/(6)`
Thus `T_(1)=(T)/(12)`
and `T_(2)=(T)/(6)`
`therefore" "T_(1) lt T_(2)`