Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Driven Oscillator

驱动振荡器

If a damped oscillator is driven by an external force, the solution to the motion equation has two parts, a transient part and a steady-state part, which must be used together to fit the physical boundary conditions of the problem.

The motion equation is of the form

运动方程的形式为

and has a general solution

并且有通解

如果一个阻尼振子受到外力驱动，运动方程的解由两部分组成，即瞬态部分和稳态部分，必须一起使用以满足问题的物理边界条件。

In the underdamped case this solution takes the form

在欠阻尼情况下，该解的形式为

The initial behavior of a damped, driven oscillator can be quite complex. The parameters in the above solution depend upon the initial conditions and the nature of the driving force, but deriving the detailed form is an involved algebra problem. The form of the parameters is shown below.

Details of parameter evaluation

参数评估细节

Examples of driven oscillators

驱动振荡器的例子

Transient solution
暂态解
 Steady-state solution
稳态解
 Expansion of above terms
上述术语的扩展
阻尼驱动振子的初始行为可能相当复杂。上述解中的参数取决于初始条件和驱动力的性质，但推导出详细形式是一个复杂的代数问题。参数的形式如下所示。
 Index

Periodic motion concepts
索引 周期性运动概念
 
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Underdamped Driven Oscillator

欠阻尼驱动振荡器

The expanded expressions for the underdamped oscillator in terms of the mass, spring constant, damping, and driving force. They are also affected by the initial values of position and velocity.

关于质量、弹簧常数、阻尼和驱动力的欠阻尼振子的扩展表达式。这些也受到初始位置和速度的影响。
 Index

Periodic motion concepts

Reference

Barger & Olsson

Marion & Thornton, Ch 3
索引 周期性运动概念 参考 Barger & Olsson Marion & Thornton, 第3章
 
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Transient Solution, Driven Oscillator

驱动振子的暂态解
The solution to the driven harmonic oscillator has a transient and a steady-state part. The transient solution is the solution to the homogeneous differential equation of motion which has been combined with the particular solution and forced to fit the physical boundary conditions of the problem at hand. The form of this transient solution is that of the undriven damped oscillator and as such can be underdamped, overdamped, or critically damped.

Examples of driven oscillators

驱动振荡器的例子
驱动谐振子的解包含瞬态部分和稳态部分。瞬态解是运动的齐次微分方程的解，它与特解结合，并被强制拟合到当前问题的物理边界条件。这种瞬态解的形式是无驱动力的阻尼振子，因此可以是欠阻尼、过阻尼或临界阻尼的。
 Index

Periodic motion concepts
索引 周期性运动概念
 
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Steady-State Solution, Driven Oscillator

稳态解，受迫振荡
The solution to the driven harmonic oscillator has a transient and a steady-state part. The steady-state solution is the particular solution to the inhomogeneous differential equation of motion. It is determined by the driving force and is independent of the initial conditions of motion.

Examples of driven oscillators

驱动振荡器的例子
驱动谐振子的解包含瞬态部分和稳态部分。稳态解是运动非齐次微分方程的特解，由驱动力决定，与运动的初始条件无关。
 Index

Periodic motion concepts
索引 周期性运动概念
 
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