The paper focuses on studying and designing of one type of dynamical systems with nonlinear restoring force. Our research revolves around the well-known Duffing equation, which describes body motions in two coupled potential wells. The Duffing equation considers that these motions are influenced by the initial speed and position of the moving body, as well as externally driven harmonic oscillations. In our paper, we propose to view the dynamical system defined by the Duffing equation as consisting of two subsystems. One subsystem defines body position and speed, while the other defines the restoring force. By applying the symmetry approach to these subsystems, we can design a generator of restoring force that is driven by the position of the moved body. Our studies demonstrate that using a controlled restoring force allows us to influence the overall system dynamics. When the gain, which determines the relationship between the body and the generator, has a positive value, the body motions are damped, whereas contrary motions become less stable with a negative gain. We explore system motions in normal and canonical spaces to showcase the potential for various implementations of the studied dynamical system. Additionally, we demonstrate the implementation of the systems in normal and canonical spaces by transforming their descriptions into a discrete-time domain and utilizing the Arduino Due demo board.