harmonic oscillations

简明释义

谐振荡

英英释义

例句

1.The analysis of harmonic oscillations 谐振荡 is crucial in understanding wave phenomena.

分析谐振荡对于理解波动现象至关重要。

2.In a spring-mass system, the mass experiences harmonic oscillations 谐振荡 when displaced from its equilibrium position.

在弹簧-质量系统中，质量在离开平衡位置时会经历谐振荡。

3.The pendulum exhibits harmonic oscillations 谐振荡 as it swings back and forth.

这个摆在前后摆动时表现出谐振荡的特性。

4.The sound produced by a tuning fork is an example of harmonic oscillations 谐振荡 in air.

调音叉产生的声音是空气中谐振荡的一个例子。

5.Many musical instruments produce sound through harmonic oscillations 谐振荡 of their strings or air columns.

许多乐器通过弦或空气柱的谐振荡产生声音。

作文

Harmonic oscillations are a fundamental concept in physics and engineering, representing the repetitive back-and-forth motion of an object about an equilibrium position. These oscillations can be observed in various systems, from simple pendulums to complex electrical circuits. Understanding harmonic oscillations (谐振荡) is crucial for analyzing the behavior of these systems and predicting their future states.At the heart of harmonic oscillations (谐振荡) lies the principle of restoring force. When an object is displaced from its equilibrium position, a force acts upon it to return it to that position. This force is often proportional to the displacement, leading to a sinusoidal motion. A classic example of this is a mass attached to a spring. When the mass is pulled down and released, it will oscillate up and down in a smooth, periodic manner.Mathematically, harmonic oscillations (谐振荡) can be described using sine and cosine functions. The general equation for a harmonic oscillator can be expressed as:x(t) = A cos(ωt + φ)where x(t) is the displacement at time t, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase constant. This equation captures the essence of harmonic oscillations (谐振荡), illustrating how the position of the oscillating object changes over time.In addition to mechanical systems, harmonic oscillations (谐振荡) are also prevalent in wave phenomena. For instance, sound waves and electromagnetic waves can be understood in terms of oscillations. In sound, the pressure variations in the air create waves that propagate through space, while in light, electric and magnetic fields oscillate perpendicularly to each other and to the direction of wave propagation.The study of harmonic oscillations (谐振荡) extends beyond theoretical applications; it has practical implications in various fields. Engineers utilize the principles of harmonic motion when designing buildings, bridges, and vehicles to ensure stability and safety under oscillatory forces such as wind or earthquakes. In electronics, oscillators are vital components in circuits, generating signals for communication devices, clocks, and other technologies.Moreover, harmonic oscillations (谐振荡) play a significant role in understanding natural phenomena. For example, the oscillations of the Earth’s atmosphere contribute to weather patterns, while the vibrations of tectonic plates can lead to earthquakes. By studying these oscillations, scientists can gain insights into the underlying mechanisms of these events and improve prediction models.In conclusion, harmonic oscillations (谐振荡) are a vital topic in both theoretical and applied sciences. They provide a framework for understanding a wide range of physical phenomena, from the simple motion of a pendulum to the complex interactions within the Earth's systems. Mastering the concept of harmonic oscillations (谐振荡) not only enhances our comprehension of the natural world but also equips us with the tools to innovate and solve real-world problems across various disciplines.

谐振荡是物理学和工程学中的一个基本概念，表示物体围绕平衡位置的反复往返运动。这些振荡可以在各种系统中观察到，从简单的摆到复杂的电路。理解harmonic oscillations（谐振荡）对于分析这些系统的行为和预测其未来状态至关重要。在harmonic oscillations（谐振荡）的核心是恢复力的原理。当物体从其平衡位置偏移时，会有一个力作用于它，使其返回到该位置。这个力通常与位移成正比，从而导致正弦运动。一个经典的例子是附着在弹簧上的质量。当质量被拉下并释放时，它将以平滑、周期性的方式上下振荡。在数学上，harmonic oscillations（谐振荡）可以用正弦和余弦函数来描述。谐振子的通用方程可以表示为：x(t) = A cos(ωt + φ)其中x(t)是时间t的位移，A是振荡的幅度，ω是角频率，φ是相位常数。这个方程捕捉了harmonic oscillations（谐振荡）的本质，说明了振荡物体的位置如何随时间变化。除了机械系统，harmonic oscillations（谐振荡）在波现象中也很普遍。例如，声波和电磁波可以用振荡来理解。在声音中，空气中的压力变化产生波动通过空间传播，而在光中，电场和磁场垂直振荡于彼此及波传播方向。对harmonic oscillations（谐振荡）的研究不仅限于理论应用；它在各个领域具有实际意义。工程师在设计建筑、桥梁和车辆时利用谐振动的原理，以确保在风或地震等振荡力下的稳定性和安全性。在电子学中，振荡器是电路中的重要组成部分，为通信设备、时钟和其他技术生成信号。此外，harmonic oscillations（谐振荡）在理解自然现象方面也发挥着重要作用。例如，地球大气的振荡会影响天气模式，而构造板块的振动可能导致地震。通过研究这些振荡，科学家可以深入了解这些事件的基本机制，并改进预测模型。总之，harmonic oscillations（谐振荡）是理论与应用科学中的一个重要主题。它们为理解从简单摆动到地球系统内复杂相互作用的广泛物理现象提供了框架。掌握harmonic oscillations（谐振荡）的概念不仅增强了我们对自然世界的理解，还为我们提供了工具，以创新和解决各个学科中的现实问题。