Question

# A particle executes simple harmonic motion (amplitude = A) between  x=-A and x=+A . The time taken for it to go from 0 to A2 is T1 and to go from A2 to A is T2. Then

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

Solution

## The correct option is A T1<T2Using  x=A sinωt For x=A2, sin ωT1=12⇒ T1=π6ω For x=A, sin ω(T1+T2) =1 ⇒ T1+T2=π2ω ⇒ T2=π2ω−T1=π2ω−π6ω=π3ω.i.e.T1< T2 Alternate method: In S.H.M., velocity of particle also oscillates simple harmonically. Speed is more near the mean position and less near the extreme position. Therefore the time taken for the particle to go from 0 to A2 will be less than the time taken to go from A2  to A. Hence T1< T2 Physics

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