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?
The principle of equipartition states that in a system in thermal equilibrium, the total energy is equally distributed among all the degrees of freedom of the system.
The simple pendulum consists of a mass attached to a string or rod, which is free to swing back and forth. The energy of the pendulum is divided between its kinetic energy, which is due to its motion, and its potential energy, which is due to its position. According to the principle of equipartition, these two forms of energy are equal at any given point in time.
Yes, the equation is E = ½mv2 + ½kx2, where E is the total energy, m is the mass, v is the velocity, k is the spring constant, and x is the displacement from equilibrium.
The principle of equipartition is closely related to the concept of temperature. In a system in thermal equilibrium, the average kinetic energy of each degree of freedom is directly proportional to the temperature. In the case of a simple pendulum, the kinetic energy of the pendulum is proportional to its velocity, which in turn is related to the temperature of the environment.
Yes, the principle of equipartition assumes that the system is in thermal equilibrium, which may not always be the case for a simple pendulum. Factors such as air resistance and friction can affect the energy distribution and may not follow the expected pattern. Additionally, at very low temperatures, quantum effects may come into play and violate the equipartition principle.