This turned out to be a fun project to animate. It worked hand in hand with easing and thankfully I didn't come across any issues animating a generic pendulum.
Prior to this task we had been shown a video which illustrated the difference between animating on an arc versus animating on a straight line, and I was happy to see how natural this movement looked on an arc.
Sequence 1 - Pendulum
Sequence 2 - Pendulum motion loop
For the second sequence I initially thought I'd do a cat's tail but ultimately decided on a dragon. The initial arc guidelines I had were placed at the tip of the tail until I realised while drawing it out that the tip would look more natural lagging behind the body of the tail, so I moved my guidelines further up the tail instead.