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The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?
- a)T and E triples
- b)T and E doubles
- c)T remains same and E becomes nine times
- d)T gets tripled and E becomes zero
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The amplitude A of a simple harmonic oscillator (with period, T and en...
E α A2 and hence the energy will become 9 times.
T is independent of A and hence no change will occur.
Hence C is the correct answer.
T is independent of A and hence no change will occur.
Hence C is the correct answer.
Most Upvoted Answer
The amplitude A of a simple harmonic oscillator (with period, T and en...
E α A2 and hence the energy will become 9 times.
T is independent of A and hence no change will occur.
Hence C is the correct answer.
T is independent of A and hence no change will occur.
Hence C is the correct answer.
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The amplitude A of a simple harmonic oscillator (with period, T and en...
Understanding Simple Harmonic Motion (SHM)
In a simple harmonic oscillator, the relationship between amplitude, period, and energy is crucial to understanding the system's behavior.
Effect on Period (T)
- The period of a simple harmonic oscillator is determined by the mass and the spring constant (for a mass-spring system) or the length and gravitational acceleration (for a pendulum).
- The formula for the period T is T = 2π√(m/k) for a mass-spring system or T = 2π√(L/g) for a pendulum.
- Importantly, the period T is independent of the amplitude A; thus, when the amplitude is tripled, the period remains unchanged.
Effect on Energy (E)
- The energy E of a simple harmonic oscillator is given by the formula E = (1/2)kA^2 for a mass-spring system.
- Therefore, if the amplitude A is tripled (A → 3A), the new energy becomes:
E_new = (1/2)k(3A)^2 = (1/2)k(9A^2) = 9 * (1/2)kA^2.
- This indicates that the energy increases by a factor of nine.
Conclusion
- Thus, when the amplitude of the oscillator is tripled:
- The period T remains the same.
- The energy E increases to nine times its original value.
In summary, the correct answer is option 'C': T remains the same, and E becomes nine times.
In a simple harmonic oscillator, the relationship between amplitude, period, and energy is crucial to understanding the system's behavior.
Effect on Period (T)
- The period of a simple harmonic oscillator is determined by the mass and the spring constant (for a mass-spring system) or the length and gravitational acceleration (for a pendulum).
- The formula for the period T is T = 2π√(m/k) for a mass-spring system or T = 2π√(L/g) for a pendulum.
- Importantly, the period T is independent of the amplitude A; thus, when the amplitude is tripled, the period remains unchanged.
Effect on Energy (E)
- The energy E of a simple harmonic oscillator is given by the formula E = (1/2)kA^2 for a mass-spring system.
- Therefore, if the amplitude A is tripled (A → 3A), the new energy becomes:
E_new = (1/2)k(3A)^2 = (1/2)k(9A^2) = 9 * (1/2)kA^2.
- This indicates that the energy increases by a factor of nine.
Conclusion
- Thus, when the amplitude of the oscillator is tripled:
- The period T remains the same.
- The energy E increases to nine times its original value.
In summary, the correct answer is option 'C': T remains the same, and E becomes nine times.
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The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer?.
The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The amplitude A of a simple harmonic oscillator (with period, T and energy, E) is tripled. What would happen to T and E?a)T and E triplesb)T and E doublesc)T remains same and E becomes ninetimesd)T gets tripled and E becomes zeroCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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