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If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle is
- a)Circular
- b)Elliptical
- c)Helical
- d)Spiral
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the motion of a particle is described by x = 5 cos(8πt), y = 5 s...
T), where x is the position of the particle and t is time in seconds, then the motion of the particle is a simple harmonic motion with an amplitude of 5 units and a period of π/4 seconds.
The position of the particle at any time t can be found by substituting the value of t in the given equation:
x = 5 cos(8t)
For example, if t = 0, then
x = 5 cos(0) = 5
This means that the particle is at its maximum position, which is 5 units to the right of its equilibrium position.
Similarly, if t = π/16, then
x = 5 cos(8π/16) = 5 cos(π/2) = 0
This means that the particle is at its equilibrium position, which is the center point of its motion.
If t = π/8, then
x = 5 cos(8π/8) = -5
This means that the particle is at its maximum position to the left of its equilibrium position.
Therefore, the motion of the particle is a simple harmonic motion with an amplitude of 5 units and a period of π/4 seconds.
The position of the particle at any time t can be found by substituting the value of t in the given equation:
x = 5 cos(8t)
For example, if t = 0, then
x = 5 cos(0) = 5
This means that the particle is at its maximum position, which is 5 units to the right of its equilibrium position.
Similarly, if t = π/16, then
x = 5 cos(8π/16) = 5 cos(π/2) = 0
This means that the particle is at its equilibrium position, which is the center point of its motion.
If t = π/8, then
x = 5 cos(8π/8) = -5
This means that the particle is at its maximum position to the left of its equilibrium position.
Therefore, the motion of the particle is a simple harmonic motion with an amplitude of 5 units and a period of π/4 seconds.
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If the motion of a particle is described by x = 5 cos(8πt), y = 5 s...
C cuz xsq+ysq=5sq
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If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer?
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If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer?.
If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle isa)Circularb)Ellipticalc)Helicald)SpiralCorrect answer is option 'C'. Can you explain this answer?.
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