受迫和阻尼振动微分方程解法探究

Solution of Forced and Damped Vibration Differential Equation

"振动"是普通物理力学中一个基本而且重要的内容,研究振动时,运动方程的求解问题较为复杂,是教学的一个难点,一般教科书都没有给出求解过程,直接给出方程的解来进行讨论.该文用复数法和试探法求出受迫振动微分方程的解.对理解"振动"的有关概念和规律有很大帮助,为"振动"方程求解提供了简明的方法.

When ＂the vibration＂ is one basic and the important content in ordinary physical mechanics, studying the vibration, the solution of motion equation is more complex, also becomes the teaching difficulty, generally the textbook has not given the solution process, but given the solution of equation to cart5, on the discus- sion directly. This article extracts the solution of forced vibration differential equation with the plural method and trial method, which is helpful to understand the related concept and the rule of ＂vibration＂, provides the concise method for the equation solution.