首先导出二自由度欠阻尼系统具有重特征值的充分必要条件,其次证明了这样的系统特征亏损的充分条件是它的两个固有频率互异,最后举例说明。本文的结果表明:与人们的某些猜想相反,欠阻尼系统有特征亏损,不是罕见的,这种现象不应忽视。 First, the necessary and sufficient conditions for eigenvalues ​​of under-damped two-degree-of-freedom systems are derived. Second, the sufficient condition for the loss of such system characteristic is proved that the two natural frequencies are different from each other. Finally, an example is given. The results of this paper show that contrary to some people’s suspicions, the underdamped system has the characteristic loss, which is not uncommon. This phenomenon should not be neglected.