The average total energy of a simple pendulum is conclusively shown to be equal to twice the average kinetic energy, as derived from the equation E = T + V = 1/2 ml²(θ'²) + mgl cos(θ). The discussion emphasizes the application of the equipartition theorem, noting that the pendulum must satisfy specific assumptions, particularly regarding thermal equilibrium. It is critical to recognize that variations in potential shape can yield different results, thus not all pendulum-like systems adhere to this conclusion. Explicit calculations of average kinetic energy through integration over one period are necessary for validation.
PREREQUISITESStudents of physics, particularly those studying classical mechanics, as well as educators and researchers interested in energy dynamics of oscillatory systems.
Then you have to show that your pendulum satisfies the assumptions going into that theorem. In particular, your pendulum is not in thermal equilibrium with anything, and a different potential shape will lead to a different result so it does not apply to all pendulum-like systems.Glenda said:Maybe use equipartition?