Oscillator with random trichotomous mass

► We consider the new type of stochastic oscillator, which has random mass fluctuations (white, dichotomous or trichotomous). ► Two first moments are calculated for an oscillator subject to an external periodic force and additive white noise. ► The second moment shows non-monotonic (resonance) dependence on parameters of an oscillator and noise, showing instability for some values of these parameters.