Modeling Single Input Single Output System using SolidThinking Activate

Few weeks back SolidThinking Activate (equivalent to Matlab Simulink) is released under its math and system modelling portfolio. Being a Simulink user thought of exploring it with the classical spring and damper system, a single input single output (SISO) system.

The system

Spring Damper System
Spring Damper System

 

Image source: wiki

 

Where,

m = 1 kg;

k = 1 N/m;

c = 0.2 N / (m/sec)

 

Governing equations by using Newton’s Third law:

∑F = m. x’’(t)

=> F(t) – k.x(t) – c.x’(t) = m.x’’(t) …………………..eq.1.1

 

Direct modelling of the differential equations:

At this point, as you know, you can directly model the eq.1.1 in ACTIVATE (or in Simulink):

 

SolidThinking Activate SISO Differential Equation Model
SolidThinking Activate SISO Differential Equation Model

 

Upon simulation, I got the response (displacement) for unit step functions as input force:

Spring Damper System Response for Differential Equation Model
Spring Damper System Response for Differential Equation Model

 

Modelling of transfer functions

You can, of course, model the system using the transfer function. And to develop a transfer function of the system, you must take Laplace transform of eq.1.1:

  F(t) – k.x(t) – c.x’(t) = m.x’’(t)

  • F(s) – k.X(s) – c.s.X(s) = m.s2.X(s)
  • X(s) / F(s) = 1 / [m.s2 + c.s + k]…………………eq.1.2

So, we got the transfer function. I used the transfer function in ACTIVATE:

Spring Damper Transfer Function Activate Model
Spring Damper Transfer Function Activate Model

And the simulation response by this method:

Spring Damper System Response for Transfer Function Activate Model
Spring Damper System Response for Transfer Function Activate Model

 

Please observe that in both the method, the max displacement value is 1.6 mm. I simulate changing the mass from 1kg to 0.5 kg, max. displacement increased to 1.8mm:

Spring Damper System Response for Reduced Mass
Spring Damper System Response for Reduced Mass

Further I tried decreasing the damping coefficient from 0.2 to 0.1 and found:

Spring Damper System Response for Reduced Damping
Spring Damper System Response for Reduced Damping

If you are an existing matlab simuink user, you will found SoildThinking ACTIVATE effortless. It has nice clean GUI and a help section with some tutorials.

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