F(t) | Guess |
or | |
roots
|
|
real and distinct | |
double real | |
complex | |
modal: |
Find eigenvalus of |
or |
,
Rayleigh
where
|
where |
speed is | |
phase roots and | Unstable, repelling |
phase roots and | stable, attracting |
both real, one >0 and one <0 | unstable saddle point |
equal roots and >0 | unstable, degenrate |
equal roots and <0 | stable, degenrate |
complex, real part>0 | unstabe, spiral out |
complex, real part<0 | stable, spiral in |
pure complex conjugrates | marginaly stable, cirlce |
time betwen |
convert: |
, assume Plug in, rewrite as , find eigens of sys,each find |
, use |
impulse |
2 equations of motions for unbalanced: and , where eq for is
, guess , we obtain perturbation: hence . Sub in ODE, generate 2 ODE's and solve for and use result to find watch for IC and resonanse. For system ID, set up and from the spectrum, find