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Question

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

A
T1<T2
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B
T1>T2
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C
T1=T2
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D
T1=2T2
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Solution

The correct option is A T1<T2
Since time period is only dependent on the length of the pendulum and acceleration due to gravity. So it will remain same. B incorrect.
Since potential energy is only dependent on the displacement from mean position, it will remain as same as previous. C incorrect.
Kinetic energy at mean position = total energy =12kA2 (this much kinetic energy is added to pendulum)
So the total energy becomes 12kA2+12kA2=kA2=12k(2A)2=12kA2
A=2A
Its new amplitude is 2 times of previous amplitude. A correct

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