Assertion and Reason on SHM Energies – Rankers Physics

Energy in SHM: Practice Problem & Solution

Assertion (A): In a SHM, kinetic and potential energies become equal when the displacement is \(\frac{1}{\sqrt{2}}\) times the amplitude. Reason (R): In SHM, kinetic energy is zero when potential energy is maximum.  
Both (A) and (R) are true and (R) is the correct explanation of (A)
Both (A) and (R) are true but (R) is not the correct explanation of (A)
Both (A) and (R) are true
(A) is true and (R) is false

Solution Explained:

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

Equating \(KE = \frac{1}{2}k(A^2 - x^2)\) and \(PE = \frac{1}{2}kx^2\) gives \(x = \frac{A}{\sqrt{2}}\). Maximum PE occurs at extremes where KE is zero. Both statements are true, but (R) does not explain (A).

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