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Question

Two particles execute S.H.M of same amplitude and frequency along the same straight line from same mean position. They cross one another without collision, when going in opposite direction, each time their displacement is half of their amplitude. The phase-difference between them is

A
0
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B
120
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C
180
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D
135
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Solution

The correct option is B 120
Since both particles have same amplitude and frequency, its equation is
x1=xmcosωtx2=xmcos(ωt+ϕ)
Crossing happens when x1=xm2
So x1=xmcosωtxm2=xmcosωtωt=π3
Similarly for x2, but it is moving in different direction so the closest value of ωt+ϕ=2π3
ωt+ϕ=2π3π3+ϕ=2π3ϕ=π3
Ans: 120 degreee

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