Summary: In this paper, the stochastic resonance of an underdamped harmonic oscillator with random mass and driven by a periodic modulated noise is investigated. The fluctuation of the oscillator mass is modeled by a dichotomous noise while the internal noise is assumed to be Gaussian. Using the Shapiro-Loginov formula and the Laplace transform technique, exact expressions of the first moment of the steady-state response and the output of the system are presented. Then some simulations are implemented to study the dependence of long-time behavior of the first moment on variety of the system parameters. It is shown that the output amplitude non-monotonically depends on the signal frequency, the noise parameters and the system parameters, which indicates the occurrences of bona fide stochastic resonance, generalized stochastic resonance and parameter-induced stochastic resonance. Furthermore, based on the exact expressions, it is demonstrated that the interplay of the mass fluctuation and the periodic modulated noise can generate some novel cooperation effects, such as double-peak resonances as well as one-valley resonances.