V2EX harmonic motion

Harmonic Motion

定义 Definition

谐和运动(简谐运动):一种随时间按正弦/余弦规律变化、并且回复力(或加速度)与位移成正比且方向相反的周期运动。最常见的例子是理想弹簧振子和小角度近似下的单摆。(在物理语境中也常用 simple harmonic motion 表达更精确的“简谐运动”。)

发音 Pronunciation

/hrmnk mon/

例句 Examples

A mass on a spring can undergo harmonic motion.
弹簧上的物体可以做谐和运动。

When damping is negligible, the system’s displacement follows harmonic motion with a constant frequency and amplitude determined by initial conditions.
当阻尼可以忽略时,系统的位移会呈现谐和运动,频率恒定,而振幅由初始条件决定。

词源 Etymology

Harmonic 源自希腊语 harmonia,本义与“和谐、协调”有关,后来引申到音乐中的“和声”,再进一步用于描述物理量呈“规则、协调”的周期变化(如正弦波形)。Motion 源自拉丁语 motio(移动、运动)。合起来,harmonic motion 字面义就是“呈和谐规律的运动”,在物理中特指正弦规律的周期运动。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • The Feynman Lectures on Physics(Richard P. Feynman 等):用谐振子与简谐运动作为理解振动与波动的核心模型。
  • Vibrations and Waves(A. P. French):以谐和运动为基础系统讲解波、共振与能量传递。
  • The Theory of Sound(Lord Rayleigh):在声学与振动理论中大量使用与谐和运动相关的数学与物理框架。
  • Classical Mechanics(Herbert Goldstein):将简谐振子作为经典力学与近似方法的重要范例反复出现。
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