Hooke's Law: F = -kx, where k is the spring constant (N/m, dimension [$MT^{-2}$]) and x is displacement from natural length.

Key Properties:

• Restoring force: always directed toward natural length
• Linear: force proportional to displacement (within elastic limit)
• Energy stored: U = \frac{1}{2}$$kx^2
• Massless spring: tension same throughout

Combinations:

• Series: 1/$k_{eq}$ = 1/$k_1$ + 1/$k_2$ (softer — more extension for same force)
• Parallel: $k_{eq}$ = $k_1$ + $k_2$ (stiffer — less extension for same force)
• Cut into n parts: each part has constant nk

Equilibrium extension: For mass m hanging from spring: $kx_0$ = mg, $x_0$ = $\frac{mg}{k}$.