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。

Simple Harmonic Motion

简谐运动

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency.

简谐运动典型地表现为弹簧上质量的运动，当该质量受到由胡克定律给出的线性弹性恢复力作用时。这种运动在时间上是正弦的，并表现出一个单一的共振频率。

Motion equations
运动方程
 Motion calculation
运动计算
 Frequency calculation
频率计算
 Motion sequence visualization
运动序列可视化
Damped oscillation
阻尼振动
 Driven oscillation
驱动振荡
Index

Periodic motion concepts
索引 周期性运动概念
 
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Simple Harmonic Motion Equations

简谐运动方程

The motion equation for simple harmonic motion contains a complete description of the motion, and other parameters of the motion can be calculated from it.

The velocity and acceleration are given by

速度和加速度由下式给出

The total energy for an undamped oscillator is the sum of its kinetic energy and potential energy, which is constant at

未阻尼振子的总能量是其动能和势能之和，该值保持不变。

Energy transformation in periodic motion
周期性运动中的能量转化
简谐运动的运动方程包含对运动的完整描述，其他运动参数可以从该方程中计算得出。
 Index

Periodic motion concepts
索引 周期性运动概念
 
HyperPhysics***** Mechanics
力学
R Nave
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Simple Harmonic Motion Calculation

简谐运动计算

The motion equations for simple harmonic motion provide for calculating any parameter of the motion if the others are known.

If the period is T =s
then the frequency is f = Hz and the angular frequency = rad/s.

如果周期是 T = s，则频率是 f = Hz，角频率为 rad/s。
中文译文中的待填/计算数值依次对应：1：t 2：f 3：af。实际数值以上方原输入框为准。

The motion is described by

该运动由
Displacement = Amplitude x sin (angular frequency x time)
简谐运动的运动方程允许在已知其他参数的情况下计算任何运动参数。位移 = 幅度 × sin(角频率 × 时间)
y
=
A
 x sin (
x sin (（专名或术语）
ω
 x
t
)
m
=
m
 x sin (
x sin (（专名或术语）
rad/s
 x
s
)

Any of the parameters in the motion equation can be calculated by clicking on the active word in the motion relationship above. Default values will be entered for any missing data, but those values may be changed and the calculation repeated. The angular frequency calculation assumes that the motion is in its first period and therefore calculates the smallest value of angular frequency which will match the other parameters. The time calculation calculates the first time the motion reaches the specified displacement, i.e., the time during the first period.

任何运动方程中的参数都可以通过点击上方运动关系中的活性词来计算。对于缺失的数据，默认值将被输入，但这些值可以被更改，并且可以重复计算。角频率的计算假设运动处于第一周期内，因此计算出的角频率是能与其它参数匹配的最小值。时间的计算是确定运动首次达到指定位移的时间，即第一周期内的时间。
 Index

Periodic motion concepts
索引 周期性运动概念
 
HyperPhysics***** Mechanics
力学
R Nave
 Go Back
返回





计算模块中未附着于文字的输入框：
中文译文中的待填/计算数值依次对应：1：y 2：a 3：om 4：ti。实际数值以上方原输入框为准。