Mass Spring Damper Example

Keywords:Theory of Control, Matlab Simulink

First of all, we will simulate a mass-spring-damper system.

We assume that there is no force involved. Lets get started. Open a new Simulink file. Our system involves two integrators (from acceleration to velocity and from velocity to position). In the Simulink window, click on Continuous.

In the right hand side you can see the integrator. Click on it and drag the block inside the window just opened. Repeat this operation as, we need two integrators. By now, your window should look like below:

To model our system we need two more gain blocks and one sumator block. We can find these two blocks in the Math section.

Right click on the first Gain block. Choose Format->Rotate Block. As this operation will rotate the block with 90 degrees (clockwise), you have to do it once more time.

Do the same for the second Gain block. Add a scope from Sinks and connect the blocks with lines.

If you take a look on the block diagram you have just constructed, it is easy to see that it represents the relationship:

where, the first gain represents the c/m term and the second one represents the term k/m.