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We demonstrate the linear frequency conversion of ferromagnetic resonance (FMR) frequency by optically excited elastic waves in a thin metallic film on dielectric substrates. Time-resolved probing of the magnetization directly witnesses magnetoelastically driven parametric second-harmonic generation, sum- and difference-frequency mixing from two distinct frequencies, as well as excitation of parametric resonances. Starting from the Landau-Lifshitz-Gilbert equations, we derive an analytical equation of an elastically driven (nonlinear) parametric oscillator and show that frequency mixing is dominated by the parametric modulation of the linear FMR oscillator. [ABSTRACT FROM AUTHOR]