阻尼振荡系统在分子动力学和经典力学研究中有着举足轻重的作用，所以其解析结果是力学研究的关键问题.但是想要得到多体系统的解析结果并不是一项容易的工作.为了得到二体问题的解析表达式，本文在计算过程中采用了拉普拉斯变换，留数定理以及卡尔丹诺 (Cardano) 公式等理论方法.精确计算表明，二体系统可分为三种情况：临界阻尼振荡、过阻尼振荡以及欠阻尼振荡，这与单体阻尼谐振子的情况非常相似.同样，这三种模式也通过判别式Δ进行分类.最后这项研究为更复杂系统的研究提供了一些线索.

Damped oscillating system is an extremely important topic in the study of molecular dynamics and classical dynamics, so the analytical result is the key problem on this system. But the exact expressions are always to obtain in many-body system. Motivated to get the two-bodys analytic expressions, Laplace transform, residual theory and Cardano formula are applied to the calculation. Accurate computations show that this system could be distinguished into three situations: critical damping oscillation, overdamped oscillation and underdamped oscillation, which is quite analogous to simple damped harmonic oscillator. Similarly, the three modes are also classified via the discriminant Δ. Finally, this study sheds some light into the topics on more complicated systems.