Hooke's Law: F = -kx

• k: spring constant $\frac{N}{m}$, dimension [$MT^{-2}$]
• x: displacement from natural length (m)
• Negative sign: force is restoring (opposite to displacement)

Key properties:

1. Spring force is a variable force (depends on extension)
2. At natural length, F = 0
3. Compression: F pushes outward; Extension: F pulls inward
4. Energy stored: U = \frac{1}{2}$$kx^2

Springs in series: 1/$k_{eq}$ = 1/$k_1$ + 1/$k_2$ (effective spring constant decreases) Springs in parallel: $k_{eq}$ = $k_1$ + $k_2$ (effective spring constant increases)

Massless spring: Tension is same throughout (like a massless string, but force depends on extension).

JEE application: When a block on a spring is in equilibrium: $kx_0$ = mg. If displaced by A from equilibrium, it oscillates with amplitude A.