Equation of SHM: Practice Problem & Solution
Assertion (A): \(x = \sin^2(\omega t)\) represents a SHM about mean position \(x = \frac{1}{2}\). Reason (R): \(a \propto -x\) is the necessary condition for SHM.
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): \(x = \sin^2(\omega t) = \frac{1 - \cos(2\omega t)}{2}\). Let \(y = x - \frac{1}{2} = -\frac{1}{2}\cos(2\omega t)\). This is SHM about \(x = \frac{1}{2}\). So (A) is true. Reason (R): For SHM, acceleration is proportional to negative displacement \(a = -\omega^2 x\). So (R) is true. However, (R) does not explain (A).
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