- #1
MuIotaTau
- 82
- 3
For a damped mechanical oscillator, the energy of the system is given by $$E = \frac{1}{2}m \dot{x}^2 + \frac{1}{2}k x^2$$ where ##k## is the spring constant. From there, I've seen it dictated that the average kinetic energy ##\langle T \rangle ## is half of the total energy of the system. This makes sense, since the energy sort of "sloshes" back and forth between kinetic and potential energy, but is there a more formal way to show this is true?