Springs are everywhere — in your mechanical keyboard, your car's suspension, your garage door, and the click mechanism of a ballpoint pen. They store and release mechanical energy, absorb shock, maintain contact force, and return systems to equilibrium. Understanding how they behave starts with one elegant linear relationship.

Hooke's Law: F = kx

The force F a spring exerts is proportional to its displacement x from its natural (free) length. The constant k is the spring rate (or stiffness), measured in N/m or lb/in. This holds true only within the elastic region — push a spring past its yield point and it permanently deforms. As a software engineer, think of Hooke's Law as a linear transfer function: input is displacement, output is force, and k is the gain.

The four major spring types:

• Compression springs — the classic coil that resists being pushed shorter. Used in valve trains, pogo sticks, and mattresses. Most common spring type by far.
• Extension (tension) springs — coils wound tightly together with hooks on each end; they resist being pulled apart. Found in garage door counterbalance systems and trampolines.
• Torsion springs — resist rotational force. The spring in a clothespin or a mousetrap is a torsion spring. For these, the law becomes τ = κθ, where τ is torque, κ is rotational stiffness, and θ is angular displacement.
• Leaf springs — flat strips of steel stacked and clamped together. Common on truck rear axles and older vehicle suspensions. They double as a structural linkage, locating the axle relative to the frame.

Practical calculation: Your car's coil spring has a rate of 35,000 N/m (a typical front spring for a sedan). If the car's front corner supports 400 kg (3,924 N of weight), how much does the spring compress at rest?

x = F / k = 3924 / 35000 = 0.112 m ≈ 112 mm

That ~11 cm of compression is your static deflection. Engineers size springs so this sits comfortably in the middle of the spring's travel, leaving room for bumps (more compression) and rebounds (extension).

Springs in series vs. parallel — just like resistors, but inverted. Two identical springs in parallel (side by side) double the effective rate: k_total = k₁ + k₂. In series (end to end), the combined spring is softer: 1/k_total = 1/k₁ + 1/k₂. This is the opposite of how resistors combine — parallel springs act like series resistors and vice versa.

Rule of thumb: The energy stored in a compressed spring is E = ½kx². Double the displacement, quadruple the energy. This is why a spring that's "only a little more compressed" can release dramatically more force — and why preloaded springs in mechanisms deserve respect during disassembly.