Particle motion in elliptical path – Rankers Physics

Equation of SHM: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:

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.

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Similar Practice Questions

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1. A particle is undergoing SHM having total mechanical energy equal to \(8\text{ J}\). At an instant its kinetic energy is found to be \(10\text{ J}\), then its potential energy at that instant is
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