Class 11 Exam > Class 11 Questions > In damped oscillations, the amplitude of osci...
Start Learning for Free
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:
- a)a0 / 2
- b)a0 / 6
- c)a0 / 9
- d)a0 / 4
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In damped oscillations, the amplitude of oscillations is reduced to on...
Damped Oscillations and Amplitude Reduction
Damped oscillations refer to a type of oscillatory motion where the amplitude of the oscillations decreases over time due to the presence of damping forces. These forces can arise from friction, air resistance, or other types of resistance within the system.
The amplitude of damped oscillations can be characterized by a decay constant, which describes how quickly the amplitude decreases over time. The decay constant is related to the damping coefficient, which is a measure of the strength of the damping forces.
In this problem, we are given that the amplitude of oscillations is reduced to one-third of its initial value after 100 oscillations. This means that after 100 oscillations, the amplitude has decayed by a factor of 3. We can use this information to find the decay constant and damping coefficient of the system.
Calculating Amplitude After 200 Oscillations
To find the amplitude of oscillations after 200 oscillations, we can use the following formula:
A = A0 * e^(-bt)
where A is the amplitude at time t, A0 is the initial amplitude, b is the decay constant, and t is the time elapsed.
We can solve for the decay constant using the fact that the amplitude has decayed by a factor of 3 after 100 oscillations:
3A0 = A0 * e^(-100b)
Simplifying this equation, we get:
e^(100b) = 3
Taking the natural logarithm of both sides, we get:
100b = ln(3)
b = ln(3) / 100
Now we can use this value of b to find the amplitude after 200 oscillations:
A = A0 * e^(-bt)
A = A0 * e^(-(ln(3)/100) * 200)
A = A0 * e^(-2ln(3)/100)
A = A0 * e^(ln(9)/100)
A = A0 * (e^(ln(9)))^(1/100)
A = A0 * 9^(1/100)
A = A0 / 9
Therefore, the amplitude of the oscillations after 200 oscillations is one-ninth of the initial amplitude, or A0/9. The correct answer is option C.
Damped oscillations refer to a type of oscillatory motion where the amplitude of the oscillations decreases over time due to the presence of damping forces. These forces can arise from friction, air resistance, or other types of resistance within the system.
The amplitude of damped oscillations can be characterized by a decay constant, which describes how quickly the amplitude decreases over time. The decay constant is related to the damping coefficient, which is a measure of the strength of the damping forces.
In this problem, we are given that the amplitude of oscillations is reduced to one-third of its initial value after 100 oscillations. This means that after 100 oscillations, the amplitude has decayed by a factor of 3. We can use this information to find the decay constant and damping coefficient of the system.
Calculating Amplitude After 200 Oscillations
To find the amplitude of oscillations after 200 oscillations, we can use the following formula:
A = A0 * e^(-bt)
where A is the amplitude at time t, A0 is the initial amplitude, b is the decay constant, and t is the time elapsed.
We can solve for the decay constant using the fact that the amplitude has decayed by a factor of 3 after 100 oscillations:
3A0 = A0 * e^(-100b)
Simplifying this equation, we get:
e^(100b) = 3
Taking the natural logarithm of both sides, we get:
100b = ln(3)
b = ln(3) / 100
Now we can use this value of b to find the amplitude after 200 oscillations:
A = A0 * e^(-bt)
A = A0 * e^(-(ln(3)/100) * 200)
A = A0 * e^(-2ln(3)/100)
A = A0 * e^(ln(9)/100)
A = A0 * (e^(ln(9)))^(1/100)
A = A0 * 9^(1/100)
A = A0 / 9
Therefore, the amplitude of the oscillations after 200 oscillations is one-ninth of the initial amplitude, or A0/9. The correct answer is option C.
Free Test
FREE
| Start Free Test |
Community Answer
In damped oscillations, the amplitude of oscillations is reduced to on...
The answer is b
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Top Courses for Class 11View all
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer?
Question Description
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer?.
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer?.
Solutions for In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be:a)a0 / 2b)a0 / 6c)a0 / 9d)a0 / 4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
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