spring constant

Meaning: The spring constant k is the stiffness of a spring: the size of the restoring force per meter of stretch or compression from its equilibrium length. A large k means a stiff spring. For an ideal spring, k stays constant within the elastic limit, and the force points back toward equilibrium, which gives the minus sign.

Equation: F = −kx, where F is the restoring force (N), k is the spring constant (N/m), and x is the displacement from equilibrium (m). Related: U = ½kx² gives the stored energy (J), and T = 2π√(m/k) gives the period (s) of a mass m (kg) on the spring.

On the MCAT: Expect a force versus displacement graph, where the slope is k, or a hanging mass at equilibrium where kx = mg. Predict that a stiffer spring gives a shorter period and higher frequency, and that doubling the stretch doubles the force but quadruples the stored energy.

Common confusion: Students think k changes when the spring is stretched farther, or that amplitude changes the period. Within Hooke's law, k is fixed by the spring, and the period depends on m and k, not on amplitude.