Physics Exam > Physics Questions > Two particles execute simple harmonic motions...
Start Learning for Free
Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :
- a)2π/3
- b)π
- c)π/6
- d)π/3
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two particles execute simple harmonic motions of the same amplitude an...
We know the S.H.M. can be written as y = 1 sin ωt = a sin θ
For first we have,
For second,
a/2= a sinθ2 ⇒ θ2 = 300
Phase difference =
For first we have,
For second,
a/2= a sinθ2 ⇒ θ2 = 300
Phase difference =
Most Upvoted Answer
Two particles execute simple harmonic motions of the same amplitude an...
The phase difference between two particles executing simple harmonic motion can be determined by comparing their displacements at a given time.
Let's assume that the amplitude of the motion is A and the frequency is ω.
When the displacement of a particle is half of its amplitude (A/2), the phase angle can be determined as follows:
x1 = (A/2) * sin(ωt + φ1)
x2 = (A/2) * sin(ωt + φ2)
At the moment when the two particles pass each other, their displacements are equal in magnitude but opposite in direction. Therefore, we can set up the following equation:
(A/2) * sin(ωt + φ1) = -(A/2) * sin(ωt + φ2)
Dividing both sides by (A/2), we get:
sin(ωt + φ1) = -sin(ωt + φ2)
Since the sine function is an odd function, we can rewrite the equation as:
sin(ωt + φ1) = sin(-(ωt + φ2))
Using the trigonometric identity for the sine of a negative angle, we have:
sin(ωt + φ1) = -sin(ωt) * cos(φ2) - cos(ωt) * sin(φ2)
Comparing the coefficients of the sine function on both sides, we can equate them:
1 = -cos(φ2)
This implies that:
cos(φ2) = -1
Since the cosine function is equal to -1 at an angle of 180 degrees or π radians, we can conclude that:
φ2 = π
Therefore, the phase difference between the two particles is π or 180 degrees.
Let's assume that the amplitude of the motion is A and the frequency is ω.
When the displacement of a particle is half of its amplitude (A/2), the phase angle can be determined as follows:
x1 = (A/2) * sin(ωt + φ1)
x2 = (A/2) * sin(ωt + φ2)
At the moment when the two particles pass each other, their displacements are equal in magnitude but opposite in direction. Therefore, we can set up the following equation:
(A/2) * sin(ωt + φ1) = -(A/2) * sin(ωt + φ2)
Dividing both sides by (A/2), we get:
sin(ωt + φ1) = -sin(ωt + φ2)
Since the sine function is an odd function, we can rewrite the equation as:
sin(ωt + φ1) = sin(-(ωt + φ2))
Using the trigonometric identity for the sine of a negative angle, we have:
sin(ωt + φ1) = -sin(ωt) * cos(φ2) - cos(ωt) * sin(φ2)
Comparing the coefficients of the sine function on both sides, we can equate them:
1 = -cos(φ2)
This implies that:
cos(φ2) = -1
Since the cosine function is equal to -1 at an angle of 180 degrees or π radians, we can conclude that:
φ2 = π
Therefore, the phase difference between the two particles is π or 180 degrees.
Free Test
FREE
| Start Free Test |
Community Answer
Two particles execute simple harmonic motions of the same amplitude an...
We know the S.H.M. can be written as y = 1 sin ωt = a sin θ
For first we have,
For second,
a/2= a sinθ2 ⇒ θ2 = 300
Phase difference =
For first we have,
For second,
a/2= a sinθ2 ⇒ θ2 = 300
Phase difference =
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer?
Question Description
Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer?.
Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer?.
Solutions for Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two particles execute simple harmonic motions of the same amplitude and frequency along the same straight line. They pass one another travelling in opposite directions, whenever their displacement is half of their amplitude. The phase difference between the two is :a)2π/3b)πc)π/6d)π/3Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup