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) gt T_(2)`
C. `T_(1)=T_(2)`
D. `T_(1)=2T_(2)`

Answer

A

Explanation

As, `y=A//2:. (A)/(2)=A sin omegaT_(2):. sin omegaT_(1)=sin((pi)/(6))`
or `T_(1)=(pi)/(6omega)` Also `A=Asinomega(T_(1)+T_(2))`
or `sinomega(T_(1)+T_(2))=1=sin((pi)/(2)) or omega(T_(1)+T_(2))=(pi)/(2)`
`T_(1)+T_(2)=(pi)/(2omega) or T_(2)=(pi)/(2omega)-(pi)/(6omega)=2T_(1)`
`:. T_(1) lt T_(2)`