# Tag Info

1 vote

### How can I interpret the normal modes of this mechanical system?

If we label the DOF's as $u$ for all of the DOF's with inertia ($u_{1}$ and $u_{2}$ in your case), and $u_{0}$ those with no associated inertia ($\alpha$ in your case), the EOM can be written in ...
• 11

### How can I interpret the normal modes of this mechanical system?

$\def \b {\mathbf}$ The EOM's are:  \b M\, \begin{bmatrix} \ddot{u}_1 \\ \ddot{u}_2 \\ 0 \\ \end{bmatrix}+\b Q\, \begin{bmatrix} {u}_1 \\ {u}_2 \\ \alpha \\ \end{bmatrix}= \...
• 12.5k

### How can I interpret the normal modes of this mechanical system?

Ok, I'm not doing the math beyond counting degrees-of-freedom (DoF), but here's my thought process: $3 x 3$ matrix: 3 dimensions should have 3 eigenvalues for 3 DoF. But you have 2 masses, so it's a 2 ...
• 35.9k

### How can I interpret the normal modes of this mechanical system?

In this example all the linkage does is convert a displacement of $u_3$ at the top to a displacement of $-\frac ba u_3$ at the bottom instantaneously so you should not expect there to be any ...
• 98k
I have not attempted to do the algebra, but I presume that you have found that the coeffeicient of $(\omega^2)^3$ in your characteristic equation is zero. To understand what this means consider the ...