We investigate the effectiveness of chirped laser pulses in exciting a multimode system, where a vibrational mode is coupled to a large number of bath modes. We solve the Liouville equation for this model numerically to investigate the roles played by laser frequency, laser intensity, pulse width, frequency sweeping rate, and bath relaxation times in inducing vibrational excitation. We investigate the range of parameters for which chirping excitation is efficient for multimode systems. In addition, we study constant-frequency excitations using the present model, revealing the special effects of phase relaxation time and the phenomenon of molecular bistability. Furthermore, we present results on quantum decoherence and assess the validity of an effective Hamiltonian method.