Questions and discussion for this lecture live here. Fire away by hitting Reply below 
Hi Sean, I don’t get why it is legit to represent the two components as two rotating vectors in the complex plane. I mean, they do not have a real part and an imaginary part, but just the former.
I surely must be missing something
@Oliviero, although we’re not generally very used to seeing it represented this way, the rotating vector on the complex plane is just another way to represent a sinusoidal oscillation.
You can see the link between the ‘phasor’ representation and the time-domain (wave) representation when you project the tip of the rotating response arrow onto the real axis - it will trace out a sinusoidal oscillation.
The benefit of the phasor (rotating arrow) representation is that it makes it easier to ‘break out’ and visualise the phase relationship between different components of the response and how the total response lags the applied force due to damping in the system. It’s actually a really nice way to visualise the response.
Don’t think about the response as having ‘an imaginary’ component, as such - the complex plane (with its one imaginary axis) is just the mathematical construct we use to frame our rotating vector representation.