Imagine a bell that has only 3 ideal resonant frequencies (no damping) and I am hitting it with a point like ideal hammer, does this mean that all of the energy of the hammer is distributed among those 3 resonances? I think not, i.e. the energy stored in the resonant modes are less than the overall energy transferred from the hammer to the bell. The hammer is like a Dirac delta function with a flat spectrum, i.e. it has a component on every frequency. So on those frequencies where the bell is non resonant, it is maximally damping, that means the energy is converted to heat. So the bell will ring forever on its 3 resonances with a total energy less than what was exchanged with the hammer. Am I wrong?