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Question

Two particles P and Q describe SHM of same amplitude A, same frequency f along the same straight line. The maximum distance between the two particles is A2. The phase difference between the particle is

A
Zero
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B
π2
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C
π6
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D
π3
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Solution

The correct option is B π2
Equation of motion of particle 1,
x1=Asin(ωt+ϕ1)
Equation of motion of particle 2,
x2=Asin(ωt+ϕ2)
At a particular instant, separation between two particles is given by,
|x1x2|=A[sin(ωt+ϕ1)sin(ωt+ϕ2)]
[sinCsinD=2cos(C+D2)sin(CD2)]
|x1x2|=2Acos(ωt+ϕ1+ϕ22)sin(ϕ1ϕ22)
Given maximum distance between two particle is A2
To maximize |x1x2|, we choose
cos(ωt+ϕ1+ϕ22)=1
A2=2Asin(ϕ1ϕ22)
sin(ϕ1ϕ22)=12
sin(ϕ1ϕ22)=sin(π4)
ϕ1ϕ22=π4
ϕ1ϕ2=π2

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