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A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.The time it will take to drop to 1/1000 of the original amplitude is close to :
- a)50s
- b)100s
- c)20s
- d)10s
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A damped harmonic oscillator has a frequency of 5 oscillations per se...
Time of half the amplitude is = 2s
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Dividing (i) by (ii) and solving, we get t = 20 s
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A damped harmonic oscillator has a frequency of 5 oscillations per se...
Frequency of the damped harmonic oscillator:
The frequency of the damped harmonic oscillator is given as 5 oscillations per second. This means that the oscillator completes 5 oscillations in one second.
Damping factor:
The amplitude of the oscillator drops to half its value for every 10 oscillations. This indicates that the oscillator is experiencing damping.
Time taken to drop to 1/1000 of the original amplitude:
We need to find the time it takes for the amplitude to drop to 1/1000 of its original value.
Let's assume the original amplitude of the oscillator is A. According to the given information, the amplitude drops to half its value after 10 oscillations. So after 10 oscillations, the amplitude becomes A/2.
To find the time taken to drop to 1/1000 of the original amplitude, we need to determine the number of times the amplitude needs to halve.
Let's calculate:
After 10 oscillations, the amplitude is A/2.
After 20 oscillations, the amplitude is (A/2)/2 = A/4.
After 30 oscillations, the amplitude is (A/4)/2 = A/8.
After 40 oscillations, the amplitude is (A/8)/2 = A/16.
After 50 oscillations, the amplitude is (A/16)/2 = A/32.
After 60 oscillations, the amplitude is (A/32)/2 = A/64.
After 70 oscillations, the amplitude is (A/64)/2 = A/128.
After 80 oscillations, the amplitude is (A/128)/2 = A/256.
After 90 oscillations, the amplitude is (A/256)/2 = A/512.
After 100 oscillations, the amplitude is (A/512)/2 = A/1024.
From the above calculations, we can observe that the amplitude drops to 1/1000 of its original value (A) after 100 oscillations.
Therefore, the time taken to drop to 1/1000 of the original amplitude is approximately 100 seconds. Hence, the correct answer is option C.
The frequency of the damped harmonic oscillator is given as 5 oscillations per second. This means that the oscillator completes 5 oscillations in one second.
Damping factor:
The amplitude of the oscillator drops to half its value for every 10 oscillations. This indicates that the oscillator is experiencing damping.
Time taken to drop to 1/1000 of the original amplitude:
We need to find the time it takes for the amplitude to drop to 1/1000 of its original value.
Let's assume the original amplitude of the oscillator is A. According to the given information, the amplitude drops to half its value after 10 oscillations. So after 10 oscillations, the amplitude becomes A/2.
To find the time taken to drop to 1/1000 of the original amplitude, we need to determine the number of times the amplitude needs to halve.
Let's calculate:
After 10 oscillations, the amplitude is A/2.
After 20 oscillations, the amplitude is (A/2)/2 = A/4.
After 30 oscillations, the amplitude is (A/4)/2 = A/8.
After 40 oscillations, the amplitude is (A/8)/2 = A/16.
After 50 oscillations, the amplitude is (A/16)/2 = A/32.
After 60 oscillations, the amplitude is (A/32)/2 = A/64.
After 70 oscillations, the amplitude is (A/64)/2 = A/128.
After 80 oscillations, the amplitude is (A/128)/2 = A/256.
After 90 oscillations, the amplitude is (A/256)/2 = A/512.
After 100 oscillations, the amplitude is (A/512)/2 = A/1024.
From the above calculations, we can observe that the amplitude drops to 1/1000 of its original value (A) after 100 oscillations.
Therefore, the time taken to drop to 1/1000 of the original amplitude is approximately 100 seconds. Hence, the correct answer is option C.
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A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.The time it will take to drop to 1/1000 of the original amplitude is close to :a)50sb)100sc)20sd)10sCorrect answer is option 'C'. Can you explain this answer?
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A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.The time it will take to drop to 1/1000 of the original amplitude is close to :a)50sb)100sc)20sd)10sCorrect answer is option 'C'. 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 damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.The time it will take to drop to 1/1000 of the original amplitude is close to :a)50sb)100sc)20sd)10sCorrect answer is option 'C'. 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 damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.The time it will take to drop to 1/1000 of the original amplitude is close to :a)50sb)100sc)20sd)10sCorrect answer is option 'C'. Can you explain this answer?.
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