Two mass damper spring system in simulink

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How can I draw a block diagram for this system? M1=M2=1kg, b1= 1N/rad/s K1=K2= 1N/rad. All initial conditions are set to zero.

Accepted Answer

Rick Rosson
Rick Rosson on 2 Oct 2015
Edited: Rick Rosson on 2 Oct 2015
You can represent each mass as a series combination of an integrator and a gain. The value of the gain will be either M or 1/M depending on how you set things up. Likewise, you can model each spring the same way, except the value of the gain will be either k or 1/k depending on your choice of input and output. Finally, the damper is just a gain without an integrator, with the value of the gain either b or 1/b.
Before trying to model the system in Simulink, it would be helpful to write down the differential equations for each element of the system. Then, using the diagram of the physical system, you can identify the equations that relate the velocities and/or forces at connection points between each pair of elements. Finally, you can figure out how to represent the entire system as a block diagram, with each input and output representing either a force or a velocity.
Remember, the constitutive relations for each component are as follows:
  • For each mass: F = m dv/dt or dv = (1/m) F dt
  • For each spring: v = (1/k) (dF/dt) or dF = k v dt
  • For the dashpot: F = bv
  1 Comment
Thomas J. M.
Thomas J. M. on 3 Oct 2015
Thank you for your very detailed answer! I appreciate your help, and I might be able to solve it now!

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