Modeling Dynamic Systems with Mathematical Modeling (2020)

How to write a mathematical model for a mechanical system. Modeling Dynamic systems can be tricky, it can be difficult to know how to write the differential equation that represents the model of the dynamic system. Modeling dynamic systems doesn't have to be difficult. We can make if more understandable by having a better idea as to how each part effects the system as a whole. This is an example of a Mechanical dynamic system. We will be modeling the dynamic system with a mathematical model using a system of equations that represent each portion of the system and explain how they work as a whole.
This is Problem B-4-5 from System Dynamics 4th edition. We will not be finding the transfer function in this video but be more focused on understanding how to write the mathematical model for the dynamic system.
There are a lot of moving parts in a dynamic system! Change my mind!
╔═╦╗╔╦╗╔═╦═╦╦╦╦╗╔═╗
║╚╣║║║╚╣╚╣╔╣╔╣║╚╣═╣
╠╗║╚╝║║╠╗║╚╣║║║║║═╣
╚═╩══╩═╩═╩═╩╝╚╩═╩═╝
Join the FUN!
/ @thedanielk.project4998

[@Karlemilstorm]

Very interesting video that greatly supplements my control theory course at university. Next time please use manual focus to avoid focus hunting

[@wldmhd]

Any difference if the damper and the spring are parallel instead of serial ?

[@Karlemilstorm]

I think you made a mistake at 8:00. "The sum of forces equals zero". Thus the sign on one side should be flipped I believe.

[@thedanielk.project4998]

If I am looking at the same part, that being the 2 equations in the second row, I used substitution from one of those to the other. They are pretty much the same equation but because the x and y, and y and z are flipped it changes the signs. This is done strictly for later substitution purposes. Hope that helps! Let me know if you think I missed something or am looking at the wrong part. Thanks!

[@alexbrightchargeai]

Why is K3 exactly the same on both sets of equations? You said one is keeping positive the other is negative, but the K3 term is identical

[@thedanielk.project4998]

K3 is technically positive in one equation and negative in the other but we wrote the equations in a way so that they can be substituted into the other equations. They both have a negative sign because in one equation we wrote -k3(z-y)=u and the other is -k3(y-z)=u. It appears they are the same because of the z and y flipping in the parenthesis. Hope that clears the confusion up but it was written that way strictly for substitution purposes.

[@RitaKumari-xf9ks]

Hello sir. What is this model aboit

[@hashirqureshi3052]

about*