利用线性变换方法求解稳态受迫振动  

Solving the steady-state forced vibrations using the linear transformation method

作　　者：宇文天浩 郝思洁 金文涛 YUWEN Tian-hao;HAO Si-jie;JIN Wen-tao(School of Astronautics,Beihang University,Beijing 100191,China;Department of Physics,Beijing Normal University,Beijing 100875,China;School of Physics,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学宇航学院,北京100191 [2]北京师范大学物理学系,北京100875 [3]北京航空航天大学物理学院,北京100191

出　　处：《大学物理》2023年第3期37-40,共4页College Physics

摘　　要：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.

关 键 词：受迫振动 稳态解 线性变换 矢量 复平面 

分 类 号：O321[理学—一般力学与力学基础]