The paper treats the semi active isolation of a single equipment, acceleration sensitive, by means of a variable elastic control device. A numerical study on a single degree of freedom (SDOF) structural model equipped with a continuously variable elastic device subjected to harmonic input is presented. The utilized control algorithm is derived by the Lyapunov method and specialized in order to obtain instantaneous optimality. In order to minimize the dynamic response of interest, i.e. the equipment absolute acceleration, some parameters that define the algorithm and the device are conveniently selected. The purpose of the paper is to investigate the optimal isolation properties of semi active variable stiffness devices with continuous control across the whole frequency spectrum. The performances of the isolated equipment are evaluated in terms of absolute acceleration transmissibility. Semi active continuous control is compared with semi active ON-OFF mode and conventional linear passive control. Results show that it is possible to choose conveniently the parameters regulating semi active continuous control in order to limit the absolute acceleration transmissibility at all the frequencies. In literature from problems concerning vibration isolation, transmissibility is alternatively defined in terms of absolute acceleration or displacement. Here, absolute displacement transmissibility is also estimated. It is observed that in case of semi active control, there are differences between the two transmissibility representations, and they do not lead to analogous results for evaluating the performance of the control system.