This paper introduces the inerter, a mechanical device that is the true dual of the spring and allows for the synthesis of passive mechanical one-port networks. Unlike the mass element, which is always connected to ground, the inerter has two terminals and can be used to translate electrical circuits into mechanical ones in an analogous way. The inerter can have negligible mass, enabling the synthesis of any arbitrary positive-real impedance using physical components with small mass compared to other structures. The inerter is applied to vibration absorption, suspension strut design, and simulated mass. The paper discusses the force–current analogy between electrical and mechanical networks, where the spring corresponds to the inductor, the damper to the resistor, and the mass to the capacitor. However, the mass element has a restrictive feature due to its connection to ground, which limits its use in mechanical network synthesis. The inerter, being a two-terminal device, avoids this restriction and allows for more flexible network synthesis. The inerter is used in three applications: vibration absorption, suspension strut design, and simulated mass. In vibration absorption, the inerter provides an alternative to traditional spring-mass systems, allowing for better control of oscillations. In suspension strut design, the inerter enables the use of third-order admittances, which can reduce oscillation in stiffly sprung systems. In simulated mass, the inerter can mimic the behavior of a mass element. The paper also discusses the synthesis of mechanical networks using the inerter, showing that classical results from electrical circuit synthesis can be applied directly to mechanical systems. The inerter allows for the realization of positive-real admittances, which are essential for passive network synthesis. The paper concludes that the inerter offers a significant advantage in mechanical network synthesis by avoiding the restrictive features of the mass element and enabling more flexible and efficient designs.This paper introduces the inerter, a mechanical device that is the true dual of the spring and allows for the synthesis of passive mechanical one-port networks. Unlike the mass element, which is always connected to ground, the inerter has two terminals and can be used to translate electrical circuits into mechanical ones in an analogous way. The inerter can have negligible mass, enabling the synthesis of any arbitrary positive-real impedance using physical components with small mass compared to other structures. The inerter is applied to vibration absorption, suspension strut design, and simulated mass. The paper discusses the force–current analogy between electrical and mechanical networks, where the spring corresponds to the inductor, the damper to the resistor, and the mass to the capacitor. However, the mass element has a restrictive feature due to its connection to ground, which limits its use in mechanical network synthesis. The inerter, being a two-terminal device, avoids this restriction and allows for more flexible network synthesis. The inerter is used in three applications: vibration absorption, suspension strut design, and simulated mass. In vibration absorption, the inerter provides an alternative to traditional spring-mass systems, allowing for better control of oscillations. In suspension strut design, the inerter enables the use of third-order admittances, which can reduce oscillation in stiffly sprung systems. In simulated mass, the inerter can mimic the behavior of a mass element. The paper also discusses the synthesis of mechanical networks using the inerter, showing that classical results from electrical circuit synthesis can be applied directly to mechanical systems. The inerter allows for the realization of positive-real admittances, which are essential for passive network synthesis. The paper concludes that the inerter offers a significant advantage in mechanical network synthesis by avoiding the restrictive features of the mass element and enabling more flexible and efficient designs.