单词	damped oscillations
释义	damped oscillations Oscillations in which the amplitude decreases with time. Consider the equation of motion , 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.
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