BME 343 - Static and Dynamic Systems

A static system is where its outputs only depends on current conditions - it’s also called memoryless

A dynamic system is where its output depends on past condition - it’s also called memory

Here is a physical example of a simple system: A spring

Visualize a perfect vertical spring with an object on top.

You want to see how far the object will be pushed up.

Would this be a static or dynamic system?

It’s a static system!

Let’s start time the moment you let go of the spring.

As you know, the force of an ideal spring is dependent on the distance is pulled right now. It doesn’t care how much you pulled it before, its force is only dependent on how much you pulled it right now.

—Now visualize on how would you make the spring dynamic? —

One way is to simply drop the object on the spring to see how much it will push it back up. Now we are introducing a time variable to the system, most obviously an initial condition.

Let’s start time the moment you let go of the object.

The spring now cares about what is happening before the object even hits the spring.

The initial height of the object and how fast it moves before it hits the spring will influence how high it will bounce.

Because the system cares about parameters in the past (most notably initial conditions), it is a dynamic system.

A good way to identify a static or dynamic system, is if you have to ask: what happened before the outcome.

An electrical example of a static and dynamic system would be a resistor and capacitor.

Visualize the resistor graph: you can see that it’s only dependent on the voltage and current.

Now visualize the capacitor graph: you can see it’s dependent on how much voltage already is applied to the capacitor. If you were to ask how much charge the capacitor had, you would first respond with “how charged was it beforehand”.

Example Problem:

Is this a static or dynamic system?

Let me help you visualize a scenario for this system: Gossiping with your friends in class about who is the cutest in school.

This system has two dynamic components: a time delay and a derivative.

The time delay can be visualize as being whispered some gossip, waiting a few seconds to see if no one is listening, and then responding back.

The derivative can be visualized as seeing how quickly someone is passing by before you respond back. If they are moving quickly, they have a high derivative. If they are moving slowly, they have a lower derivative.

(note: Derivatives are sometimes hard to visualize but we see it everyday. Derivatives is just a fancy way of saying a difference between two things. A common difference we experience is distance, which is seen as velocity or how quickly someone is moving.)

This system is dynamic in two ways!

Btw, you decided that the cutest in school is the cool kid’s dog named Mabel. She is the goodest of boys.