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We measure the frequency dependence of the mechanical quality factor (Q) of SiN membrane oscillators and observe a resonant variation of Q by more than two orders of magnitude. The frequency of the fundamental mechanical mode is tuned reversibly by up to 40% through local heating with a laser. Several distinct resonances in Q are observed that can be explained by coupling to membrane frame modes. Away from the resonances, the background Q is independent of frequency and temperature in the measured range.