This time let's have a closer look at inertial oscillation in a moving picture. Note that other than the cat stuffed toy and the pendulum, a small point is rotating as well. This is a mark thrown by a laser from outside the rotating system (the stationary system), showing the speed of the rotation.

If you compare the movement of this point to the movement of the pendulum, you can see that the laser point does one cycle for every two cycles of the pendulum, so the cycle of the inertial oscillation is

half the size

of the rotating cycle.