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Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a√2 . The initial phase difference between the particle is –
- a)zero
- b)π/2
- c)π/6
- d)π/3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two particles P and Q describe S.H.M. of same amplitude a, same freque...
x1 = a sin(ωt + ϕ1), x2 = a sin(ωt + ϕ2 )
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To maximize 
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Most Upvoted Answer
Two particles P and Q describe S.H.M. of same amplitude a, same freque...
The maximum distance between the two particles occurs when they are in opposite phases, i.e. one is at the maximum displacement while the other is at the minimum displacement.
Let the equation of motion of particle P be given by:
xP = a sin(2πft)
And the equation of motion of particle Q be given by:
xQ = a sin(2πft + φ)
Where φ is the phase difference between the two particles.
At the instant when particle P is at its maximum displacement (a), its equation of motion becomes:
xP = a
Substituting this into the equation for particle Q:
a = a sin(2πft + φ)
Simplifying,
sin(2πft + φ) = 1
2πft + φ = nπ
Where n is an integer.
At the instant when particle P is at its minimum displacement (-a), its equation of motion becomes:
xP = -a
Substituting this into the equation for particle Q:
-a = a sin(2πft + φ)
Simplifying,
sin(2πft + φ) = -1
2πft + φ = (n + 1/2)π
Where n is an integer.
Subtracting the second equation from the first:
π/2 = 1/2 π
2πft = π/2
f = 1/4π
So the frequency of the SHM is inversely proportional to the maximum distance between the particles.
Therefore, if the maximum distance between the particles is a, the frequency is f = 1/4πa.
Let the equation of motion of particle P be given by:
xP = a sin(2πft)
And the equation of motion of particle Q be given by:
xQ = a sin(2πft + φ)
Where φ is the phase difference between the two particles.
At the instant when particle P is at its maximum displacement (a), its equation of motion becomes:
xP = a
Substituting this into the equation for particle Q:
a = a sin(2πft + φ)
Simplifying,
sin(2πft + φ) = 1
2πft + φ = nπ
Where n is an integer.
At the instant when particle P is at its minimum displacement (-a), its equation of motion becomes:
xP = -a
Substituting this into the equation for particle Q:
-a = a sin(2πft + φ)
Simplifying,
sin(2πft + φ) = -1
2πft + φ = (n + 1/2)π
Where n is an integer.
Subtracting the second equation from the first:
π/2 = 1/2 π
2πft = π/2
f = 1/4π
So the frequency of the SHM is inversely proportional to the maximum distance between the particles.
Therefore, if the maximum distance between the particles is a, the frequency is f = 1/4πa.
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Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a√2 .The initial phase difference between the particle is –a)zerob)π/2c)π/6d)π/3Correct answer is option 'B'. Can you explain this answer?
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Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a√2 .The initial phase difference between the particle is –a)zerob)π/2c)π/6d)π/3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a√2 .The initial phase difference between the particle is –a)zerob)π/2c)π/6d)π/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along the same straight line. The maximum distance between the two particles is a√2 .The initial phase difference between the particle is –a)zerob)π/2c)π/6d)π/3Correct answer is option 'B'. Can you explain this answer?.
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