Question

Two particles are executing S.H.M of same amplitude and frequency along the same straight line path. They passe' each other when going in opposite direction, each time their displacement is half of their amplitude. What is the phase difference between them?

Answer 1

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$$$${{{{{{{{{{. Two particles are executing SHM with the same amplitude and frequency, but with a phase difference, and the maximum separation found is equal to amplitude. What is the phase difference?

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4 ANSWERS



Anurodh Kumar, B Sc Physics (2011)

Updated Jan 15, 2019 · Author has 123answers and 45.1k answer views

Let the first particle be at mean position at t = 0.

Equation of shm is given by

x1=Asin(ωt)x1=Asin⁡(ωt)

And for second particle equation can be written as

x2=Asin(ωt+θ)x2=Asin⁡(ωt+θ)

Distance between them

|x2−x1||x2−x1|

=|A(sin(ωt)−sin(ωt+θ))|=|A(sin⁡(ωt)−sin⁡(ωt+θ))|

=|2Acosωt+ωt+θ2sinθ2|=|2Acos⁡ωt+ωt+θ2sin⁡θ2|

=|2Asinθ2cos2×ωt+θ2|=|2Asin⁡θ2cos⁡2×ωt+θ2|

From here we find that the lenght x2−x1x2−x1 is oscillating in nature and the maximum value is given by the constant part ie 2Asinθ22Asin⁡θ2 which is eqal to A. From this we can find θθ

2Asinθ2=A2Asin⁡θ2=A

⟹θ=π3⟹θ=π3

So phase difference is π3


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