Oscillations - a simple to and fro motion. Somehow, it has become one of the most important topic in physics and engineering.

Some says that this topic has it roots in the pendulum clocks from Europe. According to Wikipedia, the pendulum clock was invented by a Dutch scientist Christiaan Huygens a few hundred years ago.

Today, the pendulum is one of the two main examples we have to study in this topic. The other is the oscillating spring.

"Oscillations" can come in all sizes and speeds. It can be the simple pendulum swinging to and fro. It can be the bus shaking violently on the road. (Yes, this often happens to the buses I have taken.) It can be the air molecules vibrating rapidly when someone speaks. It can be some machine parts repeating the same movement over and over.

But why is it important or useful? After all, we don't really use pendulum clocks anymore, except maybe for museums or decorations.

Lets look at some real life examples - starting with the violently shaking bus mentioned above. If you have never taken a bus the shakes violently whenever it starts, moves or stops, then you are lucky. It is not very nice to be in a bus when this happens.

We know this does not happen with most buses, so there must be some problem with that bus. Something in that bus's design or manufacturing makes it easy to shake violently.

A more serious example is the Tacoma bridge in the state of Washington in the USA - in the short video clip above. In 1940, strong wind caused this bridge to swing more and more, until it broke and fell into the water. Luckily, there was enough time for everyone on the bridge to escape, except for Tubby, a dog. Sadly, the owner who tried to save Tubby was forced to turn back just before the bridge collapsed.

The violently shaking bus and Tacoma Bridge disaster For the normal

So whether it is the pendulum clock, shaking bus or Tacoma Bridge, it is important to have a good understanding of the oscillating motion that can happen when these are designed and built. The pendulum clock can be made more accuratem the shaking of the bus can be reduced or avoided, and the bridge can be safe.

Two common examples of simple harmonic motion are the pendulum and the spring. These are also often used in physics questions. The idea is for students to learn some basic details of the physics and the calculations.

For example, we usually think of a spring as a wire coiled into a spiral shape. If we hang an object on the spring, pull and let go - the object would start moving up and down.

So what are we really supposed to learn about this? Surely, every child who have ever played with a spring or rubber band would know this.

Well, we need to learn why the pendulum moves left and right, and why the spring moves up and down. We need to learn why the time of one swing seems to stay the same even if we pull the weight on the spring more so that it moves over a bigger distance. We need to learn how to calculate this time. We need to learn how to calculate the position and velocity of the weight at any time ...

And we need to learn how the energy changes repeatedly between kinetic and potential energies.

And we also need to learn examples on how this type of motion is useful in real life.

Then there are also names of various features of the motion. If a stone on the string is at rest, it is said to be at the rest position. They also like to use a more difficult word - the equilibrium position. Not sure why. Maybe it is to emphasise that there is absolutely no movement because all the forces are balanced.

And what are the forces again?

For a stone attached to a hanging spring, the forces are the weight on the stone, and the pull from the spring. At first, the stone is at rest. The weight on the stone is balanced by the force from the spring.

If I pull the stone down a bit and let go, the stone would start oscillating up and down. After a while, it would oscillate less and less. Then it stops.

If I pull down a bit more, it would do the same thing, but over a slightly larger distance - or amplitude as it is normally called. No surprises here.

But if we keep increasing the amplitude and measuring the period - the up-down time for 1 cycle - we find something strange. The period of 1 up-down cycle is the same for big and small distance from the centre of oscillation.

That is quite unexpected. Surely, it should take more time if the distance is bigger? Ok, maybe it goes faster when distance the bigger because the spring got stretched more and pulls back harder.

But exactly the same period - exactly the same time for each cycle ! That is quite surprising.

And this is one important feature of simple harmonic motion.

By the way, that is also why the pendulum clock used pendulum - because we don't have to worry that the pendulum time would change for different swing angles.

I have mentioned above that resonance happens when the oscillation or vibration amplitude grows bigger and bigger. For the Tacoma Bridge, it was catastrophic. But are there good resonances?

Definitely !

When I googled "examples of useful resonances", I found these and more :

- musical instruments,
- electric circuits for sound and timing,
- ultrasound to break up gall stones
- microwave ovens to heat up water in food
- nuclear magnetic resonance to take images of organs inside our bodies
- ...

Apparently, simple harmonic motion somehow takes place in all of these examples. So it looks like simple harmonic motion is not just about pendulum and spring !

But how is that possible? Or how does the swinging or oscillation happen in these cases?

Musical instrument would be an easier example to start with. If you pluck a violin string, you hear a sound. This is because after plucking, the string continues to oscillate - move up-down of left-right - for a short while. The pitch - or frequency - you hear is the natural frequency of the string.

But this sound stops after a short while. To keep it going, you can use a bow - that horse hair ribbon that you pull over the string to make that sound. This gives energy to the string and helps it to keep vibrating and making that nice musical note.

If we bow quite hard and look closely at the violin string, we may just about see the string vibrating - or think we see it vibrating, since it would be too fast for our eyes and look like a blur.

But we would not be able to see it when microwave in the oven makes the water molecules vibrate. The frequency of the microwave in the oven is 2.45 GHz. Some websites say that it is because this is the resonance frequency of water molecules.

Actually, in this case it is not about resonance. Resonant frequency of water molecules is above 1 THz (which is 1000 GHz). The electric field the oscillating electric field in the microwave simply shakes the water molecules so much that they get hot.

You can learn these concepts and more at Dr Hock's maths and physics tuition.