I'm looking for a differential equation that responds to an driving force and which only responds if the driving force is a superposition of two frequencies?
As a counterpoint, a harmonic oscillator will respond most when it is driven by a force which has the same frequency as the oscillator. That is, when the force is in resonance with the oscillator.
I'd like to know if there is a differential equation which involves a driving force which for which the solution has the largest response when the driving force is the sum of two frequencies, such as $sin{\omega_1t} + sin{\omega_2t}$ but not when any one of the frequencies is present without the other. So for instance the solution would not respond much to $sin{\omega_1t}$ or $sin{\omega_2t}$ by themselves.
Just to be precise, let me define the response of a solution to a driving force as the long term mean of the square of the solution, $\int_T^\infty x(t)^2 dt$ where $x(t)$ is the solution of the differential equation. Also, for this definition to make sense, the driving force has to have a bounded amplitude so that if $f(t)$ is the driving force, it has to be above and below two constants for all time.