By simulating the equations of synchronous generators, virtual synchronous machines (VSM) can serve as a promising method for integrating renewable energy into the power system. However, the multi-frequency oscillations within the system inevitably compromise the stable and safe operation of the VSM. To ensure the normal operation of the VSM, it is essential to comprehensively understand the factors that affect various oscillations and propose corresponding solutions based on this understanding. To accomplish this, the article first establishes the closed-loop characteristic equation of the system. By utilizing this equation, it suggests that there are mainly three types of power oscillation components, which can be further divided into two kinds of oscillation components: low-frequency oscillations and synchronous-frequency oscillations. It is also possible to analyze how different elements in the system influence various oscillation patterns. Then the low frequency damping and synchronous frequency damping are proposed to suppress the corresponding frequency oscillations respectively. Finally, simulations in MATLAB/SIMULINK are conducted to demonstrate the accuracy of the analyses and the effectiveness of the proposed method.