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  4. A particle executes simple harmonic motion between x = - A and x = + A. The time taken for it to go fromO to A /2 is T1 and to go from A/2 to A is T2, then

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Q. A particle executes simple harmonic motion between x = - A
and x = + A. The time taken for it to go fromO to A /2 is $T_1$ and to
go from $ A/2 \, \, to \, \, A \, is \, T_2, $ then

IIT JEEIIT JEE 2001Oscillations

Solution:

. 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 O to A/2 will be less than the
time taken to go it from A/2 to A, or$ T_1 < T2 $
NOTE
From the equations of SHM we can show that
$t_1 =T_{0-A/2} =T/ 12 \, \, and \, \, t_2 = T_ { A/2 -A } = T/6 $
So, that $ t_1 +t_2 = T_{0-A } = T/4 $