A particle is executing SHM  SHM with time period T 𝑇. If time period of its total mechanical energy is T′𝑇' thenT′T𝑇'𝑇 is

The total mechanical energy of a particle executing Simple Harmonic Motion (SHM) remains constant throughout the motion. This is because the total mechanical energy is the sum of kinetic and potential energy, which continuously interchange during SHM but their sum remains constant.

Since the total mechanical energy remains constant, it doesn't have a time period. The concept of a time period applies to quantities that vary periodically, which is not the case for the total mechanical energy in SHM.

Therefore, the question as stated seems to have a misunderstanding. The time period of the total mechanical energy T' doesn't exist or it could be considered as infinity.