The total energy of a particle executing S.H.M. is:

Explanation

In simple harmonic motion (S.H.M.), the total energy is a constant sum of kinetic and potential energies, and is given by the formula E = (1/2)mω2A2. Here, E is the total energy, m is the mass, ω is the angular frequency of the oscillation, and A is the amplitude.This equation shows that the total energy is directly proportional to the square of the amplitude, which means that if the amplitude is doubled, the total energy increases by a factor of four.Incorrect options: The energy is not inversely proportional to the square of the amplitude (Option A), nor is it directly proportional to the amplitude (Option B). Option C, stating the energy is zero, is incorrect as the energy in S.H.M. is always a positive value, never zero.