Oscillations in which the amplitude decreases with time. Consider the equation of motion $m\ddot{x}=-kx-c\dot{x}$, where the first term on the right‐hand side arises from an elastic restoring force satisfying Hooke’s law, and the second term arises from a resistive force. The constants k and c are positive. The form of the general solution of this linear differential equation depends on the auxiliary equation mα‎² + cα‎ + k = 0. When c² < 4mk, the auxiliary equation has non‐real roots, and damped oscillations occur. This is a case of weak damping. When c² = 4mk, the auxiliary equation has equal roots and critical damping occurs: oscillation just fails to take place. When c² > 4mk there is strong damping: the resistive force is so strong that no oscillations take place.