A semi-active vibration control technique using piezoelectric actuators with switched inductance shunts has been studied. This technique can be used for not only vibration suppression but also energy harvesting. In order to design semi-active vibration control systems and energy harvesters using this technique efficiently, it is necessary to analyze and understand the effects of design parameters on the performance of these systems. Responses of these systems to harmonic disturbance forces can be used for performance evaluation and previous studies analyze periodic responses of semi-active vibration control systems by assuming sinusoidal displacement responses and using method of harmonic balance. However, this control technique induces rectangular control forces and the displacement responses are distorted. Enhancing the control forces leads to stronger distortion of the responses and the validity of the assumption of the previous studies becomes lost. In order to overcome this problem, the authors have proposed to use shooting method which is a numerical method to calculate periodic solutions of non-linear systems without assuming certain forms of responses. This paper presents periodic responses obtained by shooting method with an improved non-dimensional model and the periodic responses are compared with ones obtained by method of harmonic balance. Furthermore, this paper considers not only the periodic responses but also non-periodic chaotic responses obtained by long term simulations with the non-dimensional model.