From the second set, thre's more to it than just a pendulum.
You couldn't get the motion in that 3rd image without the pivot point at the top of the pendulum moving, I think.
Anything from a straight line, to a circle, going through all shapes of ellipse is possible.
You can also make that simple shape rotate, if the attachment point rotates.
Or if your pendulum is long enough and slow enough to be stationary relative to the earth's rotation - which is your camera's point of reference.