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A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]
- a)straight line passing through origin
- b)circle
- c)hyper bola
- d)ellipse
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A particle of mass m oscillates along x-axis according to equation x =...
(ωt + φ), where a is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. The displacement of the particle from its equilibrium position at any time t is given by x(t) = a sin(ωt + φ).
The velocity of the particle at any time t is the derivative of the displacement with respect to time, which is given by:
v(t) = aω cos(ωt + φ)
The acceleration of the particle at any time t is the second derivative of the displacement with respect to time, which is given by:
a(t) = -aω^2 sin(ωt + φ)
The negative sign indicates that the acceleration is in the opposite direction to the displacement. This means that when the particle is at its maximum displacement, the acceleration is zero, and when the particle passes through the equilibrium position, the acceleration is maximum.
The period of the motion is the time taken by the particle to complete one full oscillation. It is given by:
T = 2π/ω
The frequency of the motion is the number of oscillations per unit time. It is given by:
f = ω/2π
The maximum velocity of the particle is given by:
v_max = aω
The maximum acceleration of the particle is given by:
a_max = aω^2
The energy of the particle is the sum of its kinetic and potential energies. At any time t, the total energy of the particle is given by:
E(t) = (1/2)mv^2 + (1/2)kx^2
where k is the spring constant. The energy is constant throughout the motion, and is equal to the total energy at any other time.
The velocity of the particle at any time t is the derivative of the displacement with respect to time, which is given by:
v(t) = aω cos(ωt + φ)
The acceleration of the particle at any time t is the second derivative of the displacement with respect to time, which is given by:
a(t) = -aω^2 sin(ωt + φ)
The negative sign indicates that the acceleration is in the opposite direction to the displacement. This means that when the particle is at its maximum displacement, the acceleration is zero, and when the particle passes through the equilibrium position, the acceleration is maximum.
The period of the motion is the time taken by the particle to complete one full oscillation. It is given by:
T = 2π/ω
The frequency of the motion is the number of oscillations per unit time. It is given by:
f = ω/2π
The maximum velocity of the particle is given by:
v_max = aω
The maximum acceleration of the particle is given by:
a_max = aω^2
The energy of the particle is the sum of its kinetic and potential energies. At any time t, the total energy of the particle is given by:
E(t) = (1/2)mv^2 + (1/2)kx^2
where k is the spring constant. The energy is constant throughout the motion, and is equal to the total energy at any other time.
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A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect 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 A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect 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 A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect answer is option 'D'. Can you explain this answer?.
A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect 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 A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect 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 A particle of mass m oscillates along x-axis according to equation x = a sinωt. The nature of the graph between momentum and displacement of the particle is [NEET Kar. 2013]a)straight line passing through originb)circlec)hyper bolad)ellipseCorrect answer is option 'D'. Can you explain this answer?.
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