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A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will be
- a)A straight line
- b)A circle
- c)An ellipse
- d)A parabola
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A particle is subjected to two mutually perpendicular simple harmonic ...
(4t) and y = 4 cos(3t). Find the amplitude and phase angle of the resultant motion.
We can write the x and y coordinates as:
x = 2sin(4t)
y = 4cos(3t)
To find the resultant motion, we need to add the x and y components:
r = √(x^2 + y^2)
r = √[(2sin(4t))^2 + (4cos(3t))^2]
r = √(4sin^2(4t) + 16cos^2(3t))
r = √(4(1-cos^2(4t)) + 16cos^2(3t))
r = √(20cos^2(3t) + 4)
Now we can find the amplitude by taking the maximum value of r:
Amplitude = √(20+4) = √24 = 2√6
To find the phase angle, we can use the formula:
tan(θ) = y/x
θ = tan^-1(y/x)
θ = tan^-1(4cos(3t)/2sin(4t))
θ = tan^-1(2cot(4t)cos(3t))
The phase angle will vary with time, so we cannot give a specific value. We can, however, say that the phase angle will be equal to the angle whose tangent is 2cot(4t)cos(3t).
We can write the x and y coordinates as:
x = 2sin(4t)
y = 4cos(3t)
To find the resultant motion, we need to add the x and y components:
r = √(x^2 + y^2)
r = √[(2sin(4t))^2 + (4cos(3t))^2]
r = √(4sin^2(4t) + 16cos^2(3t))
r = √(4(1-cos^2(4t)) + 16cos^2(3t))
r = √(20cos^2(3t) + 4)
Now we can find the amplitude by taking the maximum value of r:
Amplitude = √(20+4) = √24 = 2√6
To find the phase angle, we can use the formula:
tan(θ) = y/x
θ = tan^-1(y/x)
θ = tan^-1(4cos(3t)/2sin(4t))
θ = tan^-1(2cot(4t)cos(3t))
The phase angle will vary with time, so we cannot give a specific value. We can, however, say that the phase angle will be equal to the angle whose tangent is 2cot(4t)cos(3t).
Community Answer
A particle is subjected to two mutually perpendicular simple harmonic ...
A article is subject to two mutually perpendicular
simple harmonic simple harmonic motion such it's x and y
coordinate an ellipse ans
simple harmonic simple harmonic motion such it's x and y
coordinate an ellipse ans
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A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer?
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A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer?.
A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin ωt y = 2 sin (ωt + π/4) The path of the particle will bea)A straight lineb)A circlec)An ellipsed)A parabolaCorrect answer is option 'C'. Can you explain this answer?.
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