GCSE物理：什么是简谐振动simple harmonic motion（SHM）？思维导图

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:

Thefrequency, f,单位时间内完成振动的次数，单位是赫兹hertz (Hz).

The frequency and the period can therefore be related as:

Thedisplacementof an oscillating particle is the distance the particle has been moved from its equilibrium position.

一个振动质点的位移就是距离其平衡位置的距离。

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

振幅就是指点质点距离其平衡位置的最大距离。

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

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.

是最基本也是最简单的一种机械振动。当某物体进行简谐运动时，物体所受的力跟位移成正比，并且力总是指向平衡位置。

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

思考下面这个简单的简谐运动模型的例子，这将有助于我们进一步理解SHM

Now remember that displacement, velocity and acceleration are all vectors, and as a result, direction is important. Let's choose anything in theup-wardsdirection to bepositive, anythingdownwardsto benegative.(If you decide to do the opposite, it doesn't matter - just stick to your choice.)

记住，简谐运动中，位移，速度，和加速度都是向量，方向的选择也是尤为重要的。让我们选向上为正方向，向下为相反方向

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).

如果我们事先已经把弹簧下面的物块拉离平衡位置，那么整个物理系统此时处于的位置就是最大位移

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

此时，速度为零

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

但是拥有最大的加速度，指向为负方向

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图展示了速度与加速度在简谐运动中如何变化，也就是速度与加速度，位移与速度和加速度与质量之间的关系，为了准确理解，我们就需要知道这个质点在每一点的运动规律与离开开始位置的距离。

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.

质点移动到平衡点位置时，位移为零，速度达到最大，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.

质点移动到最低点时，质点速度为零，位移为负，加速度达到最大。

1. Thevelocity, 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.)

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.)

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.

特别需要注意的是，简谐振动的周期是一个与其振幅无关的物理量，它不随振幅的变化而变化。

There are two common examples of simple harmonic motion:

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

简谐运动也被用来解释晶体内的原子振动规律，与弹簧振子的规律是一样的。

其实生活中还有很多的运动的规律都可以归咎为简谐运动，所以说我们对于物理的理解可不要仅仅停留在卷面上啊。

最后祝大家在A Level考试中都能拿到A*！！！

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