JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Elasticity & SHM

Which graph represents the difference between total energy and potential energy of a particle executing SHM Vs it's distance from mean position?

Answer: (D)

Solution

The difference asked for is total energy minus potential energy, which is the kinetic energy of the oscillator:

E - U = \frac{1}{2} m ω^{2} (A^{2} - x^{2}) .

As a function of displacement this is a downward curve: it reaches its maximum at the mean position

x = 0

and falls to zero at the extreme positions

x = \pm A

. The graph that rises to a single peak at the centre and meets the axis at

\pm A

represents this relation.

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option