Hooke's Law: F = -kx
- k: spring constant (N/m), dimension [MT^{-2}]
- x: displacement from natural length (m)
- Negative sign: force is restoring (opposite to displacement)
Key properties:
- Spring force is a variable force (depends on extension)
- At natural length, F = 0
- Compression: F pushes outward; Extension: F pulls inward
- Energy stored: U = (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.