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.