SATHEE: Oscillations - Result Question 16

Oscillations - Result Question 16

19. Two simple harmonic motions act on a particle. These harmonic motions are $x = A \cos (ω t + δ)$ , $y = A \cos (ω t + α)$ when $δ = α + \frac{π}{2}$ , the resulting motion is

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(a) a circle and the actual motion is clockwise

(b) an ellipse and the actual motion is counterclockwise

(d) a circle and the actual motion is counter clockwise

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Answer:

Correct Answer: 19. (d)

Solution:

(d) $x = A \cos (ω t + δ)$

$y = A \cos (ω t + α)$

When $δ = α + \frac{π}{2}$

$x = A \cos (\frac{π}{2} + ω t + α)$

$x = - A \sin (ω t + α)$

Squaring (1) and (2) and then adding $x^{2} + y^{2} = A^{2} [\cos^{2} (ω t + α) + \sin^{2} (ω t + α)]$ or $x^{2} + y^{2} = A^{2}$ , which is the equation of a circle. The present motion is anticlockwise.

Oscillations - Result Question 16

19. Two simple harmonic motions act on a particle. These harmonic motions are $x = A \cos (ω t + δ)$ , $y = A \cos (ω t + α)$ when $δ = α + \frac{π}{2}$ , the resulting motion is

Answer:

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Oscillations - Result Question 16

19. Two simple harmonic motions act on a particle. These harmonic motions are x=Acos⁡(ωt+δ), y=Acos⁡(ωt+α) when δ=α+π2, the resulting motion is

Answer:

Engineering Preparation

Medical Preparation

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Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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19. Two simple harmonic motions act on a particle. These harmonic motions are $x = A \cos (ω t + δ)$ , $y = A \cos (ω t + α)$ when $δ = α + \frac{π}{2}$ , the resulting motion is