This question already has an answer here:
For resonance to occur, is it true that the force lags behind the motion by $\pi/2$? I saw some notes written that the motion lags behind the force by $\pi/2$ which makes no sense to me. As I watched many videos and I worked out the motion, it always happens before the force pushes. E.g. if the force is $F=\cos\omega t$ and $x = A\cos(\omega t -\pi/2)$, is it true that force lags behind the motion?
If it's $\pi/2$ , does there happen anything special?
Also, I realised that if there is no damping, we can only get 180 or 0 phase difference, which is quite counterintuitive to me. Can anyone give any example to help me feel better?