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Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will be
- a)A straight line inclined at 45º to the x-axis
- b)An ellipse with the major axis along x-axis
- c)An ellipse with the major axis along y-axis
- d)A circle
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two simple harmonic motions with the same frequency act on a particle ...
Sure, I can explain the answer to this question.
The answer is d) A circle.
When two simple harmonic motions with the same frequency act on a particle at right angles, the resultant motion is a circle. This is because the two motions add together to form a Lissajous figure, which is a closed curve. The shape of the Lissajous figure depends on the amplitudes and the phase difference of the two motions.
In this case, the amplitudes of the two motions are equal and the phase difference is π/2. This means that the Lissajous figure will be a circle. The centre of the circle will be at the origin, and the radius of the circle will be equal to the sum of the amplitudes of the two motions.
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Two simple harmonic motions with the same frequency act on a particle ...
The phase difference between two simple harmonic motions is given by the equation:
Δφ = φ₂ - φ₁
where Δφ is the phase difference, φ₂ is the phase of the second motion, and φ₁ is the phase of the first motion.
Since the two motions are at right angles to each other, we can represent them using the equations:
x = A₁cos(ωt + φ₁)
y = A₂cos(ωt + φ₂)
where x and y are the displacements along the x and y axes, A₁ and A₂ are the amplitudes of the motions, ω is the angular frequency (2πf) with f being the frequency, and t is the time.
Given that the amplitudes are equal (A₁ = A₂ = A), the equations become:
x = Acos(ωt + φ₁)
y = Acos(ωt + φ₂)
The phase difference can be calculated by subtracting the phase of the first motion from the phase of the second motion:
Δφ = φ₂ - φ₁
Since the amplitudes are equal, we can set x = y and solve for the phase difference:
Acos(ωt + φ₁) = Acos(ωt + φ₂)
Taking the inverse cosine of both sides:
ωt + φ₁ = ωt + φ₂
Simplifying:
φ₂ - φ₁ = 0
Therefore, the phase difference between two simple harmonic motions with the same frequency and equal amplitudes acting on a particle at right angles is zero.
Δφ = φ₂ - φ₁
where Δφ is the phase difference, φ₂ is the phase of the second motion, and φ₁ is the phase of the first motion.
Since the two motions are at right angles to each other, we can represent them using the equations:
x = A₁cos(ωt + φ₁)
y = A₂cos(ωt + φ₂)
where x and y are the displacements along the x and y axes, A₁ and A₂ are the amplitudes of the motions, ω is the angular frequency (2πf) with f being the frequency, and t is the time.
Given that the amplitudes are equal (A₁ = A₂ = A), the equations become:
x = Acos(ωt + φ₁)
y = Acos(ωt + φ₂)
The phase difference can be calculated by subtracting the phase of the first motion from the phase of the second motion:
Δφ = φ₂ - φ₁
Since the amplitudes are equal, we can set x = y and solve for the phase difference:
Acos(ωt + φ₁) = Acos(ωt + φ₂)
Taking the inverse cosine of both sides:
ωt + φ₁ = ωt + φ₂
Simplifying:
φ₂ - φ₁ = 0
Therefore, the phase difference between two simple harmonic motions with the same frequency and equal amplitudes acting on a particle at right angles is zero.
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Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer?.
Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will bea)A straight line inclined at 45º to the x-axisb)An ellipse with the major axis along x-axisc)An ellipse with the major axis along y-axisd)A circleCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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