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Question

Two particles undergo SHM along parallel lines with the same time period (T) and equal amplitudes. At a particular instant. one particle is at its extreme position while the other is at its mean position. They move the same direction. They will cross each other after a further time of

A
T8
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B
3T8
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C
T6
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D
4T3
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Solution

The correct option is B 3T8
For a particle executing SHM, the displacement of the particle is given by
x=asin(ωt+ϕ)
From the data given in the question, Let us suppose that one of the particle starting from extreme position will start from point B
Let the equation of particle starting from point B be
x1=acosωt
Let the equation of particle starting from point O' moving towards A' be
x2=asinωt
Two particles cross eachother when
x1=x2
acosωt=asinωt
tanωt=1 ωt=3π4
Using ω=2πT, we can say that,
2πTt=3π4t=3T8
Thus, option (b) is the correct answer.

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