NEET Physics Question - Oscillation

Assertion (A): \(x = A sin \omega t\) & \(y = B cos \omega t\) In the above co-ordinates particle moves in elliptical path.

Reason (R): A periodic motion can always be expressed as a sum of infinite number of harmonic motions with appropriate amplitude.

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

Assertion (A) is true: From \(x = A sin \omega t\) and \(y = B cos \omega t\), we get \(\left( \frac{x}{A} \right)^2 + \left( \frac{y}{B} \right)^2 = 1\), which is an ellipse. Reason (R) is true: Fourier's theorem states any periodic motion can be decomposed into harmonic components. However, (R) does not explain why the given equations describe an ellipse.

Rankers Physics

Particle motion in elliptical path

Solution:

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