In laser display applications, the necessity to create images free of distortions imposes specific requirements on the motion of scanning devices. We present an approach of a scanning micromirror operation that is aimed to fulfill the requirements of motion linearity, high operational frequency and low actuation voltages. The operational mode incorporates a contact event between the mirror and an elastic constraint followed by a bouncing event and a subsequent inversion of motion. A stable limit cycle with voltage-dependent frequency and triangular response signal is obtained by the application of an actuation voltage which is piecewise constant in time. Approximate expressions relating the frequency and amplitude of the response with the actuating voltage are obtained by energy balance method. The influence of contact losses on the response as well as the stability of the limit cycle are studied numerically.