Spring Potential Energy

Spring obeys Hooke's law: F = −kx (restoring force, opposite to displacement).

Elastic potential energy stored in a stretched/compressed spring: U = ½kx², where x is the displacement from natural length.

Energy stored is ALWAYS positive (x² is positive).

Conservation of energy: ½mv² + ½kx² = constant (for ideal spring-mass system, no friction).

At maximum extension/compression: KE = 0, PE = max. At natural length (passing through): KE = max, PE = 0.

Hooke's law fails for very large extensions — spring may deform plastically or break.

Springs in series: 1/k_eq = 1/k₁ + 1/k₂ (softer combination). Parallel: k_eq = k₁ + k₂ (stiffer).

Used in: oscillators, shock absorbers, vehicle suspensions, accelerometers, energy storage.