A particle executes simple harmonic motion between `x = -A and x = + A`. The time taken for it to go from `0 to A//2 is T_1 and to go from A//2 to (A) is (T_2)`. Then.

Options

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

Explanation

`x=A sin omega t`
`(A)/(2)=A sin omega T_(1)` ……(`1`)
`(A)/(sqrt(2))=A sin omega (T_(1)+T_(2))`…..(`2`)
From eq. (`1`), `omega T_(1)=(pi)/(6)`
From eq. (`2`), `omega(T_(1)+T_(2))=(pi)/(4)`
`:. (T_(1)+T_(2))/(T_(1))=(6)/(4)`
`:. T_(1)=2T_(2)`