Understanding Resonance Through the Spring and Mass Analogy

Resonant circuits are a foundational technology in many high-performance electronic systems, enabling efficient energy control and transfer. A helpful way to visualize resonance is by comparing electrical behavior to mechanical motion. Here, we’ll break down resonant circuits using a spring-and-mass analogy and show how this applies to the fundamental LC tank circuit.  

Capacitor as a Spring 

Mechanically, storing electric charge in capacitors is much like stretching a spring. In a spring system, the force you apply stretches the spring a certain distance, determined by its spring constant. In electrical terms, force is analogous with voltage, displacement with charge, and spring constant with capacitance. The more voltage applied, the more charge the capacitor stores, just like stretching a spring farther with more force. 

Inductor as a Mass

Inductance is the tendency of a wire or trace to resist change when electric current flows through, sometimes called electromagnetic inertia. Inductance is analogous to a mass that naturally resists changes in velocity. It takes effort to accelerate a mass, and it takes voltage to change the current in an inductor. Like mass resisting acceleration, inductors resist changes in current. 

Resonator as a Mass on a Spring 

Continuing the analogy, when a mass is suspended from a spring, pulled down, and released, it bounces up and down at its natural frequency. This is an example of mechanical resonance. However, resonance isn’t limited to mechanics. Resonators are defined by their behavior rather than their physical form.  

In electrical systems, the energy oscillation between electric and magnetic fields is resonance too. A resonator, made from a capacitor and inductor, naturally oscillates at its preferred frequency. It’s far easier to excite at this frequency, and it effectively filters signals to select that resonance while rejecting others. Resonators will select their resonant frequency and reject the rest, even when given a complex input.  

This spring-and-mass framework helps us visualize how electrical resonators behave and understand why they’re used to isolate or maintain specific frequencies in a circuit.  

For example, an LC circuit, also known as a resonant tank circuit, consists of an inductor and a capacitor connected together like the mass connected to a spring (Figure 1).  

Figure 1: An LC resonant circuit (left) stores and exchanges energy between the electric field of the capacitor (C) and the magnetic field of the inductor (L). During energy oscillation (right), current (i) creates a magnetic field (B) in the inductor, while the capacitor builds and released electric field energy (E). 

Understanding resonance through the spring-and-mass analogy is more than just a thought exercise. When you think of energy “bouncing” between a capacitor and an inductor, it becomes easier to predict how design changes will impact system behavior. This foundation sets the stage for real-world applications like power converters, wireless charging systems, and RF filters. 

For more on foundational concepts and RF filters, read our filter basics ebook.