I'm performing an experiment with a 2D double pendulum, and in part of it I want to investigate the normal modes of the double pendulum, where the pendula are not of equal length or of equal mass. My question is - how will I actually know when I've successfully excited a normal mode?
I start by setting the initial angles to be in (roughly) the correct proportion to one another in order for the initial setup to be an eigenvector, but of course once I release the pendulum there is a slight 'jolt' which means I can't be sure the initial conditions were exactly an eigenvector (of course, realistically I'm only going to be closely approximating one). Then, once data is recorded I can generate a phase portrait with the computer, and the phase portrait I see when I get quite close to an eigenvector looks kind of like a tilted cylinder (sorry, don't know how to post a Matlab graph here). Is there a way to tell from this phase portrait (with the angles $\theta_1$ and $\theta_2$) whether I've hit a normal mode or not? Would appreciate some help.
(ie. if someone could post a picture of a phase portrait of the normal modes of a double pendulum, so that I know what I'm looking for, that would be very appreciated)