物体的受迫振动是大学物理力学部分基础且重要的内容.受迫振动在一定时间后会达到稳定状态，而该稳态下受迫振动方程的解是理解后续课程内容——共振现象的基础，具有重要的意义.本文利用线性变换方法详细求解受迫振动稳态解，相比于常规解析法，更加简洁和直观，且有助于学生深入理解线性代数在解决物理问题中的应用.

 The forced vibration of an object is a fundamental and important part of Mechanics in college physics. The forced vibration reaches a steady state after a certain time, and solving the force-vibration equation in this steady state is the basis for understanding the resonance phenomenon, the subsequent content in the course, which is of great significance. In this paper, the linear transformation method is used to solve the steady-state forced-vibration equation. Compared with the conventional analytical method, it is more concise and intuitive, and also helpful for the students to deeply understand the application of linear algebra in solving physical problems.