In this work, a numerical analysis has been carried out to study the nonlinear dynamics of a system with pneumatic artificial muscle (PAM). The system is modeled as a single degree-of-freedom system and the governing nonlinear equation of motion has been derived to study the various responses of the system. The system is subjected to hard excitation and hence the subharmonic and superharmonic resonance conditions have been studied. The second-order method of multiple scales (MMS) has been used to find the response, stability, and bifurcations of the system. The effect of various system parameters on the system response has been studied using time response, phase portraits, and basin of attraction. In these responses, while the saddle node bifurcation is found in both super and subharmonic resonance conditions, the Hopf bifurcation is found only in superharmonic resonance condition. By changing different system parameters, it has been shown that the response with three periods leads to chaotic response for superharmonic resonance condition. This study will find applications in the design of PAM actuators.