How can I simulate a spring mass damping system without singularity error in Simulink?

I have been given the following assignment:

We have a spring-mass-dampening system that has only one degree of freedom. Basically hanging down. The mass of the object is 10 kg. It is attached to a spring that has the spring constant of 21 000 N.

The system is being disturbed with a sine wave force, which pushes the mass to the direction of its movement (basically down). The angular frequency of the force is 45.8 radians per second and the amplitude is 500 Newtons.

Now, the dampening force of the system is the following:

Dampening force

I am supposed to simulate the system in Simulink and find out the amplitude of the vibration the system will settle to permanently during 10 seconds.

The issue is, my simulation meets a singularity.

Here is my attempt:

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The error is here: enter image description here

I am following the given formulas, so I don't know how to avoid the error.

I am really at loss. What am I doing wrong? Why isn't the simulation working? Should I add the dampening differently?

Any help is greatly appreciated.

Answer 1

[Sam Chak]

Hi @Abdurrahman Faig

From the Simulink model, the dynamics can be reconstructed as

and then rearranged to

.

This nonlinear term is causing the numerical simulation to explode, though in reality, it doesn't happen.

I'm not a spring person, But I think this should work.

.

So, you will need the absolute value block and the product block.