The stochastic resonance phenomenon in a harmonic oscillator with randomizing damping coefficient by asymmetric dichotomous noise is investigated. By using the random average method and Shapiro-Loginov formula, the exact solution of the average output amplitude gain (OAG) is obtained. It is applicable to a stable under-damped, critical-damped or over-damped oscillator. Numerical results show that OAG depend non-monotonically not only on the intensity and the correlation time but also on the asymmetry of the random damping in a stable oscillator in detail, that is, stochastic resonance occurs. The maximum OAG can be achieved in the proper noise. The effect of asymmetric dichotomous noise on OAG versus frequency is similar to decreasing the damping coefficient.
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