JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Elasticity & SHM

The displacement is sinusoidal with $x=0$ at $t=0$, so the potential energy $U=\frac{1}{2}k{x}^2$ begins at zero, rises to a maximum each time the particle reaches an extreme position, and falls back to zero whenever the displacement is zero. Because $U\propto x^2$ it is never negative, so its graph is a succession of identical positive humps that touch the time axis at $t=0$ and at every later instant the displacement vanishes, with period half that of the displacement. The correct plot shows these non-negative humps meeting the axis at the marked points.