Why is max power below natural frequency

Question

I can't understand why intuitively the max power is at the natural frequency. We were told in our notes that the power absorbed is exactly equal to the rate at which energy is dissipated. Yet, if we assume a system with damping the maximum amplitude does not occur at the natural frequency so why is most energy being dissipated at a frequency which has a lower amplitude than the frequency that gives the max amplitude? ($$E\propto A^{2}$$)

I understand the reason why max power occurs at the resonance frequency (because velocity is in phase with the force) but just not why there is maximum energy dissipated. Thanks.

Answer 1

In a sinusoidaly forced RLC circuit, the maximum charge and energy on the capacitor occurs at a frequency just below resonance. The current changes very little, but there is more time on each cycle to charge the capacitor. The maximum voltage and energy on the inductor occurs just above resonance. The rate of change of the current is a little higher. The current, voltage, and rate of energy dissipation on the resistor is at a maximum at the resonate frequency. I would guess that similar things would happen with the potential energy, kinetic energy, and drag on a forced, damped harmonic oscillator.