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Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff??
Verified Answer
Two particles executing SHM of same amplitude of 20cm with same period...
Explanation:
Let the wave equation of both the particles is,
x = Asin(ωt) and
x = Asin(ωt + Ф)
where A = amplitude = 20 cm for both the particles
ω = angular velocity = same for both the particles(because period is same)
Ф = phase difference.
Distance between the two particles is given by,
d = Asin(ωt + Ф) - Asin(ωt)
=> d = A[2sin(Ф/2)cos((2ωt+Ф)/2)]
clearly we will get a maximum value when cos((2ωt+Ф)/2) = maximum = 1
hence,
d = 2A[sin(Ф/2)]
=> 20 = 2x20[sin(Ф/2)]
=> [sin(Ф/2)] = 1/2
=> Ф/2 = π/6
=> Ф = π/3
Hence the phase difference between the two particles will be π/3 radians.
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
Two particles executing SHM of same amplitude of 20cm with same period...
Introduction:
In simple harmonic motion (SHM), particles oscillate back and forth about an equilibrium position. The phase difference between two particles executing SHM can be determined by considering their amplitudes, periods, and maximum distance.
Given:
Amplitude of SHM = 20 cm
Period of SHM = same for both particles
Maximum distance between the particles = 20 cm
Understanding Phase Difference:
Phase difference represents the fraction of a complete cycle by which one particle is ahead of the other in its oscillatory motion. It is usually measured in radians or degrees.
Determining Phase Difference:
To determine the phase difference between the two particles, we need to consider their maximum distances and the relationship between phase difference and maximum distance.
Relationship between Phase Difference and Maximum Distance:
The phase difference between two particles executing SHM can be calculated using the formula:
Phase Difference = (2π * Maximum Distance) / Wavelength
Here, the wavelength is the distance covered in one complete cycle of SHM. Since the period of SHM is the same for both particles, the wavelength will also be the same.
Calculating Wavelength:
The wavelength can be calculated using the formula:
Wavelength = 2 * Amplitude
Given that the amplitude is 20 cm, the wavelength will be:
Wavelength = 2 * 20 cm = 40 cm
Calculating Phase Difference:
Using the calculated wavelength and the given maximum distance, we can now determine the phase difference between the two particles.
Phase Difference = (2π * Maximum Distance) / Wavelength
Substituting the values:
Phase Difference = (2π * 20 cm) / 40 cm
Phase Difference = π rad
Hence, the phase difference between the two particles executing SHM with the given conditions is π radians.
Summary:
Two particles executing SHM with the same amplitude and period along the same line, and with a maximum distance of 20 cm between them, have a phase difference of π radians. This phase difference represents the fraction of a complete cycle by which one particle is ahead of the other in its oscillatory motion.
In simple harmonic motion (SHM), particles oscillate back and forth about an equilibrium position. The phase difference between two particles executing SHM can be determined by considering their amplitudes, periods, and maximum distance.
Given:
Amplitude of SHM = 20 cm
Period of SHM = same for both particles
Maximum distance between the particles = 20 cm
Understanding Phase Difference:
Phase difference represents the fraction of a complete cycle by which one particle is ahead of the other in its oscillatory motion. It is usually measured in radians or degrees.
Determining Phase Difference:
To determine the phase difference between the two particles, we need to consider their maximum distances and the relationship between phase difference and maximum distance.
Relationship between Phase Difference and Maximum Distance:
The phase difference between two particles executing SHM can be calculated using the formula:
Phase Difference = (2π * Maximum Distance) / Wavelength
Here, the wavelength is the distance covered in one complete cycle of SHM. Since the period of SHM is the same for both particles, the wavelength will also be the same.
Calculating Wavelength:
The wavelength can be calculated using the formula:
Wavelength = 2 * Amplitude
Given that the amplitude is 20 cm, the wavelength will be:
Wavelength = 2 * 20 cm = 40 cm
Calculating Phase Difference:
Using the calculated wavelength and the given maximum distance, we can now determine the phase difference between the two particles.
Phase Difference = (2π * Maximum Distance) / Wavelength
Substituting the values:
Phase Difference = (2π * 20 cm) / 40 cm
Phase Difference = π rad
Hence, the phase difference between the two particles executing SHM with the given conditions is π radians.
Summary:
Two particles executing SHM with the same amplitude and period along the same line, and with a maximum distance of 20 cm between them, have a phase difference of π radians. This phase difference represents the fraction of a complete cycle by which one particle is ahead of the other in its oscillatory motion.
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Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff??
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Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff?? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff?? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff??.
Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff?? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff?? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position.The max. dist. b/w the two is 20cm.what is their phase diff??.
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