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Question

# Two particles executes SHM of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions. Each time their displacement is half of their amplitude. The phase difference between them is :

A
30o
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B
60o
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C
90o
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D
120o
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Solution

## The correct option is D 120oLet two simple harmonic motions arey=asinωt;y=asin(ωt+ϕ)In first case a2=asinωt⇒sinωt=12∴cosωt=√32In second casea2=asin(ωt+ϕ)⇒12[sinωt.cosϕ+cosωtsinϕ]⇒12[12cosϕ+√32sinϕ]⇒1−cosϕ=√3sinϕ⇒(1−cosϕ)2=3sin2ϕOn solving we getcosϕ=+1 or cosϕ=−12i.e., ϕ=0 or ϕ=120o

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