Characterization of the work done by a periodic external force on an overdamped harmonic oscillator with frequency fluctuation is studied. Results indicate that the instantaneous power with periodic variations of time shows asymmetry. It is also revealed that the work done by a periodic external force on the system in one period with the variation of multiplicative noise intensity exhibits non-monotonic behavior. Whether the system shows the coexistence of energetic stochastic resonance and suppression or not is determined by the sign of the correlation coefficient between the multiplicative noise and the additive noise.