Display omitted •Realising a linear elastic oscillator using an inherently nonlinear stiffness configuration.•Achieving a strong geometrical nonlinear damping characteristic.•Prototyping a test-rig device for validation and damping insight.•Proposing an alternative design solution to classical linear oscillators. This paper proposes a paradigm shift in the perspective of designing nonlinear oscillators, i.e., the exploitation of nonlinearity to achieve a linear behaviour to good engineering purposes. An elastic suspension with four inclined springs is studied, which has an inherently strong geometric nonlinear stiffness characteristic. Such a configuration has attracted remarkable research efforts in last couple of years, because, compared to other classical nonlinear spring configurations, it has more design parameters, which can be wisely selected to attain a tailored force–displacement characteristic. A particular relationship among these parameters is found so that the overall characteristic becomes exactly linear. Compared to the use of classical linear springs mounted along the direction of motion, the proposed configuration with inclined springs has the potential to allow more freedom in the dimensioning of an engineering device. Also, while the equivalent spring obtained is linear, the equivalent damping is not, and this has the potential advantage of practically realising a linear elastic behaviour with the benefit of geometrical nonlinear damping. Experiments are performed for validation on a prototype device, and results confirm the linear behaviour predicted by the theoretical analysis.