NEET Exam > NEET Questions > A particle executes simple harmonic oscillati...
Start Learning for Free
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]
- a)T/8
- b)T/12
- c)T/2
- d)T/4
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A particle executes simple harmonic oscillation with an amplitude a. T...
Displacement from the mean position
According to problem y = a/2
This is the minimum time taken by the particle to travel half of the amplitude from the equilibrium position.
Most Upvoted Answer
A particle executes simple harmonic oscillation with an amplitude a. T...
Understanding Simple Harmonic Motion (SHM)
In simple harmonic motion, a particle oscillates around an equilibrium position with a specific amplitude and period. Key parameters include:
- Amplitude (a): The maximum displacement from the equilibrium position.
- Period (T): The time taken for one complete cycle of motion.
Objective of the Problem
We need to find the minimum time taken by the particle to travel half of the amplitude (a/2) from the equilibrium position.
Position Equation in SHM
The position of the particle in SHM can be described by the equation:
- x(t) = a * sin(ωt)
where ω = 2π/T (angular frequency).
Finding the Time to Reach Half Amplitude
To find the time taken to reach a displacement of a/2:
- Set x(t) = a/2:
a/2 = a * sin(ωt)
- Simplifying gives:
1/2 = sin(ωt)
- This implies:
ωt = π/6 (since sin(π/6) = 1/2)
Calculating Time
Now, we can find t:
- t = (π/6) / ω
- Substitute ω = 2π/T:
t = (π/6) / (2π/T) = T/12
Conclusion
The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is T/12. Thus, the correct answer is option B: T/12.
In simple harmonic motion, a particle oscillates around an equilibrium position with a specific amplitude and period. Key parameters include:
- Amplitude (a): The maximum displacement from the equilibrium position.
- Period (T): The time taken for one complete cycle of motion.
Objective of the Problem
We need to find the minimum time taken by the particle to travel half of the amplitude (a/2) from the equilibrium position.
Position Equation in SHM
The position of the particle in SHM can be described by the equation:
- x(t) = a * sin(ωt)
where ω = 2π/T (angular frequency).
Finding the Time to Reach Half Amplitude
To find the time taken to reach a displacement of a/2:
- Set x(t) = a/2:
a/2 = a * sin(ωt)
- Simplifying gives:
1/2 = sin(ωt)
- This implies:
ωt = π/6 (since sin(π/6) = 1/2)
Calculating Time
Now, we can find t:
- t = (π/6) / ω
- Substitute ω = 2π/T:
t = (π/6) / (2π/T) = T/12
Conclusion
The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is T/12. Thus, the correct answer is option B: T/12.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer?
Question Description
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer?.
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer?.
Solutions for A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is[2007]a)T/8b)T/12c)T/2d)T/4Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET 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