Capillary-gravity waves in an inviscid liquid exhibit second- or sub-harmonic resonance at precise frequencies. When the container performs small periodic vertical vibrations, either wave may also experience Faraday ('parametric') excitation. Equations describing this situation are derived, incorporating slight detuning from two-wave and Faraday resonances. Similar Equations arise in other physical contexts. With Faraday forcing to the wave with lower frequency, the evolution equations (without detuning) are transformable To the corresponding unforced equations, the general solution of which is known.
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