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

 

 

l  Oscillation振蕩

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

完成一次完整的機(jī)械振動(dòng)所用的時(shí)間叫做一個(gè)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(gè)包含很多次振蕩次數(shù)的時(shí)間，那么周期就是：

The frequency, f, 單位時(shí)間內(nèi)完成振動(dòng)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(gè)振動(dòng)質(zhì)點(diǎn)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(diǎn)質(zhì)點(diǎn)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(jiǎn)諧運(yùn)動(dòng)

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(jiǎn)單的一種機(jī)械振動(dòng)。當(dāng)某物體進(jìn)行簡(jiǎn)諧運(yùn)動(dòng)時(shí)，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(gè)簡(jiǎn)單的簡(jiǎn)諧運(yùn)動(dòng)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(jiǎn)諧運(yùn)動(dòng)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(gè)物理系統(tǒng)此時(shí)處于的位置就是最大位移
 

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

此時(shí)，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?yàn)樨?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(jiǎn)諧運(yùn)動(dòng)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(gè)質(zhì)點(diǎn)在每一點(diǎn)的運(yùn)動(dòng)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(diǎn)移動(dòng)到平衡點(diǎn)位置時(shí)，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(diǎn)移動(dòng)到最低點(diǎn)時(shí)，質(zhì)點(diǎn)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(shí)候，是簡(jiǎn)諧運(yùn)動(dòng)停止的時(shí)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(shí)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(duì)稱一樣。
 

 

Definition of Simple Harmonic Motion: 簡(jiǎn)諧運(yùn)動(dòng)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(gè)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(yùn)動(dòng)規(guī)律就是簡(jiǎn)諧運(yùn)動(dòng)。
 

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(jiǎn)諧振動(dòng)的周期是一個(gè)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(jiǎn)諧運(yùn)動(dòng)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(jiǎn)諧運(yùn)動(dòng)也被用來解釋晶體內(nèi)的原子振動(dòng)規(guī)律，與彈簧振子的規(guī)律是一樣的。
 

其實(shí)生活中還有很多的運(yùn)動(dòng)的規(guī)律都可以歸咎為簡(jiǎn)諧運(yùn)動(dòng)，所以說我們對(duì)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*?。?！
 

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