JEE Physics 2023 Question with Solution

Given: A particle executes simple harmonic motion, and we need the variation of kinetic energy ($KE$) with displacement $x$ from the mean position to the extreme position.

Find: The nature of the graph between $KE$ and $x$.

In simple harmonic motion, total mechanical energy remains constant, and kinetic energy depends on displacement.

Also, the potential energy in simple harmonic motion varies as:

Hence, kinetic energy varies with the square of displacement, so the $KE$ versus $x$ graph is parabolic.

Therefore, the correct option is A.

Given: The particle is in simple harmonic motion.

Find: The shape of the graph of $KE$ versus $x$.

From the extracted solution, kinetic energy is related to displacement through the energy expression. Since the displacement term appears as $x^2$, the dependence is quadratic.

A quadratic dependence of a quantity on displacement gives a parabola when plotted against $x$.

Therefore, the graph is a parabola, so the correct option is A.