GCSE物理：什么是簡諧振動simple harmonic motion（SHM）？

 

l  Oscillation振蕩

指某一可觀測量的值關(guān)于中心值（常為平衡點）往復(fù)變化，或可觀測量在兩個態(tài)或多個態(tài)之間往復(fù)變化，常指隨時間的變化。常見的例子是單擺和交流電。振蕩也常稱作振動。

完成一次完整的機(jī)械振動所用的時間叫做一個周期 time period, T. 單位是秒。

   If a number of oscillations are involved we can work out the time period by dividing the total time taken by the number of oscillations completed:

如果題中給出一個包含很多次振蕩次數(shù)的時間，那么周期就是：

The frequency, f, 單位時間內(nèi)完成振動的次數(shù)，單位是赫茲 hertz (Hz).

The frequency and the period can therefore be related as:

周期與頻率的關(guān)系：

The displacement of an oscillating particle is the distance the particle has been moved from its equilibrium position.

一個振動質(zhì)點的位移就是距離其平衡位置的距離。

The amplitude of an oscillation is the maximum displacement of the vibrating object from the equilibrium position (its usual position).

振幅就是指點質(zhì)點距離其平衡位置的最大距離。

Note: Always check the x-axis on the graph, as it is easy to confuse wavelength and time period on diagrams!

l  Simple Harmonic Motion 簡諧運動

Simple Harmonic Motion (SHM) is a particular type of oscillation. It is useful because its time period stays the same even when its amplitude changes.

是最基本也是最簡單的一種機(jī)械振動。當(dāng)某物體進(jìn)行簡諧運動時，物體所受的力跟位移成正比，并且力總是指向平衡位置。

Lets think about a simple example of  SHM to work out the relationship between displacement, velocity and acceleration:

思考下面這個簡單的簡諧運動模型的例子，這將有助于我們進(jìn)一步理解SHM

Now remember that displacement, velocity and acceleration are all vectors, and as a result, direction is important. Let's choose anything in the up-wards direction to be positive, anything downwards to be negative. (If you decide to do the opposite, it doesn't matter - just stick to your choice.)

記住，簡諧運動中，位移，速度，和加速度都是向量，方向的選擇也是尤為重要的。讓我們選向上為正方向，向下為相反方向

If we set this system oscillating by lifting the mass and letting it go, then the system starts with: Maximum positive displacement (because it's above the middle).

如果我們事先已經(jīng)把彈簧下面的物塊拉離平衡位置，那么整個物理系統(tǒng)此時處于的位置就是最大位移

Zero velocity (it's not moving at the first instant).

此時，速度為零

Maximum negative acceleration (because it is about to start moving down).

但是擁有最大的加速度，指向為負(fù)方向

The interaction below shows how velocity and acceleration change in simple harmonic motion. It shows the relationship between velocity and acceleration.  The displacement, velocity and acceleration of the mass are related as shown above. To draw these, think about what the object is doing at each point as it oscillates from the start position described above.

下面的相互作用力示意圖展示了速度與加速度在簡諧運動中如何變化，也就是速度與加速度，位移與速度和加速度與質(zhì)量之間的關(guān)系，為了準(zhǔn)確理解，我們就需要知道這個質(zhì)點在每一點的運動規(guī)律與離開開始位置的距離。

As it passes through the equilibrium position on the way down it's at maximum speed down (negative), its displacement is zero and because the spring is at its equilibrium position, there is no resultant force on the mass so it is not accelerating.

質(zhì)點移動到平衡點位置時，位移為零，速度達(dá)到最大，不受力。

At the bottom, the mass stops momentarily as it changes direction, so velocity is zero. The displacement is a maximum in the negative direction, so the acceleration is a maximum in a positive direction as the spring tries to shorten again.

質(zhì)點移動到最低點時，質(zhì)點速度為零，位移為負(fù)，加速度達(dá)到最大。

1. The velocity, v, is zero where there are stationary points at the peaks and troughs of the displacement graph and the velocity is a maximum when the displacement is zero. (Don't forget the gradient of the displacement graph will equal velocity.)

速度為零的時候，是簡諧運動停止的時候，位于波谷與波峰反映在位移與速度的圖像上，換句話說就是速度等于零的時候位移達(dá)到最大。

2. The displacement and acceleration graphs are 180 degrees out of phase and therefore look like a mirror image of each other in the time axis. (Don't forget the gradient of the velocity graph will equal acceleration.)

位移與加速度的相位相差180度，就像鏡面對稱一樣。

Definition of Simple Harmonic Motion: 簡諧運動正式定義

A body is undergoing SHM when the acceleration on the body is proportional to its displacement, but acts in the opposite direction.

如果一個物體在外力作用下，其加速度與它的位移成正比例關(guān)系，并且其所受力的方向與位移的方向相反，那么它的運動規(guī)律就是簡諧運動。

Acceleration is proportional to displacement

加速度與位移成正比例關(guān)系

a α - s

It's also important to note that for SHM, the time period of the oscillations is constant and doesn't change even if the amplitude is changing.

特別需要注意的是，簡諧振動的周期是一個與其振幅無關(guān)的物理量，它不隨振幅的變化而變化。

There are two common examples of simple harmonic motion:

有兩種典型的做簡諧運動的例子

Where m = mass (kg) and   k = spring constant (Nm-1)	Where L = length of pendulum (m) g   = acceleration due to gravity (ms-2)

SHM is used to explain the behaviour of atoms in a lattice, which oscillate like masses on springs.

簡諧運動也被用來解釋晶體內(nèi)的原子振動規(guī)律，與彈簧振子的規(guī)律是一樣的。

其實生活中還有很多的運動的規(guī)律都可以歸咎為簡諧運動，所以說我們對于物理的理解可不要僅僅停留在卷面上啊。

最后祝大家在A Level考試中都能拿到A*?。。?/span>

上述就是今天介紹的主要內(nèi)容，如果對此內(nèi)容有疑問，歡迎在線咨詢我們的課程顧問老師，A+國際教育中心是國內(nèi)領(lǐng)先的國際課程輔導(dǎo)機(jī)構(gòu)，專注于為中小齡學(xué)員提供國際課程輔導(dǎo)，包括ks1-ks3、GCSE、IGCSE/Pre-A、A-Level、AP、IB等課程學(xué)科輔導(dǎo)，同時為申請英美澳加等國家私立初高中的學(xué)生提供入學(xué)考試輔導(dǎo)，幫助學(xué)生順利入讀國外優(yōu)秀私立學(xué)校。目前在北京、英國、美國分別設(shè)有授課中心。