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If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ;
Most Upvoted Answer
If a simple pendulum has significant amplitude (up
to a factor of 1/e...
Understanding Average Life Time of a Damped Pendulum
When analyzing a simple pendulum experiencing damping due to viscous drag, the average life time, τ, is a crucial concept. Here’s a detailed breakdown of the scenario:
Viscous Drag and Damping
- The pendulum bob experiences a damping force that is proportional to its velocity. This can be represented mathematically as F_d = -b * v, where:
- F_d is the damping force,
- b is the constant of proportionality,
- v is the velocity of the bob.
Exponential Decay of Amplitude
- The amplitude of the pendulum decreases over time due to damping. The amplitude becomes significant only for a limited duration, specifically from t = 0 to t = τ.
- The condition for significant amplitude is defined as reaching 1/e of the original amplitude.
Average Life Time Calculation
- The average life time (τ) can be derived from the relationship between damping and the decay of amplitude.
- For small damping, the average life time τ is effectively the time it takes for the amplitude to decay significantly, leading to the formula:
τ = 0.693 / b.
Conclusion
- Among the options provided, the correct expression for the average life time of the pendulum experiencing viscous damping is (2) 0.693/b.
- This highlights the inverse relationship between the damping constant (b) and the average life time (τ); as b increases, τ decreases, indicating that stronger damping leads to a quicker reduction in amplitude.
This understanding of the average life time is essential in various applications, including engineering and physics, where the behavior of oscillatory systems under damping is crucial.
When analyzing a simple pendulum experiencing damping due to viscous drag, the average life time, τ, is a crucial concept. Here’s a detailed breakdown of the scenario:
Viscous Drag and Damping
- The pendulum bob experiences a damping force that is proportional to its velocity. This can be represented mathematically as F_d = -b * v, where:
- F_d is the damping force,
- b is the constant of proportionality,
- v is the velocity of the bob.
Exponential Decay of Amplitude
- The amplitude of the pendulum decreases over time due to damping. The amplitude becomes significant only for a limited duration, specifically from t = 0 to t = τ.
- The condition for significant amplitude is defined as reaching 1/e of the original amplitude.
Average Life Time Calculation
- The average life time (τ) can be derived from the relationship between damping and the decay of amplitude.
- For small damping, the average life time τ is effectively the time it takes for the amplitude to decay significantly, leading to the formula:
τ = 0.693 / b.
Conclusion
- Among the options provided, the correct expression for the average life time of the pendulum experiencing viscous damping is (2) 0.693/b.
- This highlights the inverse relationship between the damping constant (b) and the average life time (τ); as b increases, τ decreases, indicating that stronger damping leads to a quicker reduction in amplitude.
This understanding of the average life time is essential in various applications, including engineering and physics, where the behavior of oscillatory systems under damping is crucial.
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If a simple pendulum has significant amplitude (up
to a factor of 1/e...
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If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ;
Question Description
If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ; for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ; covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ;.
If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ; for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ; covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to t = s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :- (m = 1kg) (1) 2 / b(2) 0.693/b (3) b (4) 1/ b"the blocks means τ;.
Solutions for If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ; in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ; defined & explained in the simplest way possible. Besides giving the explanation of
If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ;, a detailed solution for If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ; has been provided alongside types of If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ; theory, EduRev gives you an
ample number of questions to practice If a simple pendulum has significant amplitude (up
to a factor of 1/e of original) only in the period
between t = 0 s to t = s, then may be called the
average life of the pendulum. When the spherical
bob of the pendulum suffers a retardation (due to
viscous drag) proportional to its velocity, with 'b' as
the constant of proportionality, the average life time
of the pendulum is (assuming damping is small)
in seconds :- (m = 1kg)
(1)
2
/ b(2)
0.693/b (3) b (4)
1/
b"the blocks means τ; tests, examples and also practice JEE tests.
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