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3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle?
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3. A particle moves in x - y plane according to the rule, x = Asinwt a...
The Motion of a Particle in the x-y Plane
The motion of a particle in the x-y plane can be described by two equations: x = Asin(ωt) and y = Acos(ωt + π/2), where A represents the amplitude of motion, ω is the angular frequency, and t is the time. Let's break down the given equations and understand the motion of the particle in detail.
Equation for x:
The equation x = Asin(ωt) represents the motion of the particle along the x-axis. Here are the key points related to this equation:
- Amplitude (A): The amplitude A determines the maximum displacement of the particle from its equilibrium position on the x-axis. It is the distance between the maximum and minimum values of x.
- Angular frequency (ω): The angular frequency ω determines the rate at which the particle oscillates along the x-axis. It is related to the time period T of the motion by the equation ω = 2π/T, where T is the time taken for one complete oscillation.
- Time (t): The variable t represents the time at which we want to determine the position of the particle along the x-axis.
Equation for y:
The equation y = Acos(ωt + π/2) represents the motion of the particle along the y-axis. Here are the key points related to this equation:
- Amplitude (A): Similar to the x-equation, the amplitude A determines the maximum displacement of the particle from its equilibrium position on the y-axis.
- Angular frequency (ω): The angular frequency ω determines the rate at which the particle oscillates along the y-axis. It is the same as the angular frequency in the x-equation.
- Time (t): The variable t represents the time at which we want to determine the position of the particle along the y-axis.
Motion of the Particle:
By simultaneously solving the equations for x and y, we can determine the position of the particle at any given time. The particle moves in a circular path in the x-y plane, with its center at the origin (0, 0). Here are some key points regarding the motion of the particle:
- Circular Path: The particle moves in a circular path due to the sinusoidal nature of the x and y equations. The radius of the circular path is equal to the amplitude A.
- Phase Difference: The phase difference between the x and y equations determines the initial position of the particle on the circular path. In this case, the phase difference is π/2, which means the particle starts from the maximum value of y when x is at its equilibrium position.
- Time Period: The time period T of the motion is the time taken for one complete revolution of the particle along the circular path. It can be calculated using the formula T = 2π/ω, where ω is the angular frequency.
In conclusion, the given equations describe the motion of a particle in the x-y plane. The particle moves in a circular path with its center at the origin. The position of the particle at any given time can be determined by solving the equations for x and y simultaneously. The amplitude, angular frequency, and phase difference determine the characteristics of the motion, such as the radius of the circular path and the initial position of the particle.
The motion of a particle in the x-y plane can be described by two equations: x = Asin(ωt) and y = Acos(ωt + π/2), where A represents the amplitude of motion, ω is the angular frequency, and t is the time. Let's break down the given equations and understand the motion of the particle in detail.
Equation for x:
The equation x = Asin(ωt) represents the motion of the particle along the x-axis. Here are the key points related to this equation:
- Amplitude (A): The amplitude A determines the maximum displacement of the particle from its equilibrium position on the x-axis. It is the distance between the maximum and minimum values of x.
- Angular frequency (ω): The angular frequency ω determines the rate at which the particle oscillates along the x-axis. It is related to the time period T of the motion by the equation ω = 2π/T, where T is the time taken for one complete oscillation.
- Time (t): The variable t represents the time at which we want to determine the position of the particle along the x-axis.
Equation for y:
The equation y = Acos(ωt + π/2) represents the motion of the particle along the y-axis. Here are the key points related to this equation:
- Amplitude (A): Similar to the x-equation, the amplitude A determines the maximum displacement of the particle from its equilibrium position on the y-axis.
- Angular frequency (ω): The angular frequency ω determines the rate at which the particle oscillates along the y-axis. It is the same as the angular frequency in the x-equation.
- Time (t): The variable t represents the time at which we want to determine the position of the particle along the y-axis.
Motion of the Particle:
By simultaneously solving the equations for x and y, we can determine the position of the particle at any given time. The particle moves in a circular path in the x-y plane, with its center at the origin (0, 0). Here are some key points regarding the motion of the particle:
- Circular Path: The particle moves in a circular path due to the sinusoidal nature of the x and y equations. The radius of the circular path is equal to the amplitude A.
- Phase Difference: The phase difference between the x and y equations determines the initial position of the particle on the circular path. In this case, the phase difference is π/2, which means the particle starts from the maximum value of y when x is at its equilibrium position.
- Time Period: The time period T of the motion is the time taken for one complete revolution of the particle along the circular path. It can be calculated using the formula T = 2π/ω, where ω is the angular frequency.
In conclusion, the given equations describe the motion of a particle in the x-y plane. The particle moves in a circular path with its center at the origin. The position of the particle at any given time can be determined by solving the equations for x and y simultaneously. The amplitude, angular frequency, and phase difference determine the characteristics of the motion, such as the radius of the circular path and the initial position of the particle.
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3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle?
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3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle?.
3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3. A particle moves in x - y plane according to the rule, x = Asinwt and y = a cos(wt pi/2)) Straightlin The particle?.
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