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Question

A particle executes simple harmonic motion between x = - A and x = + A .The time taken by 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 = 2 T2
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Solution

The correct option is B T1< T2
(a) The equation of SHM, when it starts swinging from the mean position, is y=Asinωt .
At mean position, y=0, t=0 .....(1)

A2=Asinωt2 or sinωt2=12=sinπ6

ωt2=π6 or t2=π6ω .....(2)

At y=A time for travel from 0 to A=t3

A=Asinωt3

or sinωt3=1=sinπ2 or t3=π2ω .....(3)

T1=t2t1=π6ω .....(4)

T2=t3t2=π2ωπ6ω=π3ω .....(5)

T1T2=π6ωπ3ω=3ω6ω=12 or T1T2=12

T1<T2

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