UPSC NDA 2 2016 General Ability Solved Paper

Concept:Simple harmonic motion (SHM) is periodic motion about a mean position where the restoring force is directly proportional to displacement and opposite in direction.Explanation:The displacement of a particle in SHM is given by $y = A \sin(\omega t + \phi)$.Differentiating twice gives acceleration: $a = \frac{d^{2}y}{dt^{2}} = -\omega^{2} y$.Thus, the magnitude of acceleration is $|a| = \omega^{2} |y|$.Since $\omega = 2\pi f$, we have $|a| = 4\pi^{2} f^{2} |y|$, so acceleration is proportional to the square of the frequency.Among the given options: (A) is false because acceleration is always opposite to displacement, not necessarily to velocity. (C) is false because speed is maximum at the mean position, where acceleration is zero. (D) is false because potential energy is maximum at the extremes, where acceleration is also maximum. (B) states acceleration is proportional to the frequency – although the exact relation involves the square of frequency, the other options are clearly incorrect, making B the intended correct choice.Answer:Option B.