Q. A particle executes simple harmonic motion between $x = - A\ and\ x = + A$. The time taken for it to go from 0 to $\frac{A}{2}\ is\ T_{1}$ and to go from $\frac{A}{2}\ to\ A\ is\ T_{2}$. Then
A) $T_{1} < T_{2}$
B) $T_{1} > T_{2}$
C) $T_{1} = T_{2}$
D) $T_{1} = 2T_{2}$
Explanation
(a) In SHM, velocity of particle also oscillates simple harmonically. Speed is more near the mean position and less near the extreme positions.
Therefore, the time taken for the particle to go from 0 to $\frac{A}{2}$ will be less than the time taken to go it from $\frac{A}{2}\ to\ A.$
Hence, $T_{1} < T_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.