Two Degree of Freedom (2DOF) Problem Without Damping - Equations of Motion (EOMs)

[Alliban]

In order to avoid confusion I always draw a force in positive direction in a sketch. If it is directed vice versa, then it has to be negative. Thus, the significance of the sign is clearly defined (with respect to the coordinate system).
The stiffness matrix may be derived in an alternative procedure: Coefficient ij is the (reaction) force at location i due to a displacement of unity at location j, whereas displacements at locations not equal to j are zero.

[JohnnyYenn]

Thank you! have been trying to find this problem all day! :D

[AJ-etvf]

Thank you! Great work and awesome educational video ❤️❤️

[jathooon]

Thank you, your explanation has helped me a lot in the final test, but the sound is very low

[yotor]

thank you for your explanations It help me.

[jesusreignonhigh]

I think it can mitigate confusion if you explain how is k2*(x1-x2)? There should be an assumption of x1 > x2. And the FBD should show how the movement agrees with the assumption. Otherwise, that force direction would be questionable as well.

[joellapaz]

I had the doubt of why the force on the right side of m1 was k2(x2-x1). I think is because x2 - x1 corresponds to the equivalent strech that spring k2 is feeling. X2 refers to the tension by m2 and -x1 refers to compression by m1.

[MATLABTALKS]

Nice Video, Which software you used for tutorial writting?

[harivigneshan]

can you explain me how to decide the direction of motion?

[sayanjitb]

Dear sir, i just checked out your tutorial on coulomb damping and there you considered single degree of freedom, and here you just taking care of 2 masses system and therefore 2-DOF, My question is on what basis are we able to decide the number of degrees of freedom. I read that number of square terms in total energy terms results in degree of freedom. but I can not able to apply the the same here! could you please sort this out!
TIA

[akmalhamdan]

need to know how to solve all those matrix form. do you have that video?

[coolbotic]

I keep getting confused with the difference between x1 and x2. e.g. for the Freebody for m1 can you imagen it as -k2x1 as this is the force opposing/pushing back from the extension x1 and then +k2x2 as this spring force pulling the mass from the extension x2. i.e. have two spring forces for k2 in each direction or is this not a good way to think about it?

[Buildings]

I dont understand this matrix notation.
Can anyone point me in the direction of an explanation ?

[solonicsom]

why you are using the same direction for K1 and K2? should we only that direction?

[kmankl]

Why is it x1-x2 as opposed to x2 - x1?

[CesarLopez]

Any hint on 2DOF with damping? I am stuck trying to solve for the State -form: x_dot=Ax +Bu and y=Cx + Du... Help please.

[hadramihamdan]

on mass 1 why is the force on spring k2 (forcespring k2)= k2(x1-x2)? why it isnt k2(x2-x1) ?
srry just wondering because on somesituation i found out the solution is x2-x1 rather than x1-x2

[AV-bpbc]

Will it have two number of natural frequencies?

[pareshecho]

pls explain how was the matrix formed. ??? :/

[paarths.]

Won't this be easier to try with the Lagrangian if I may ask?