Here is a relatively simple exercise that utilizes the principles of key extremes, arc path of action, slo-in and slo-out, and repeating cycles.  The ideas behind a pendulum swing can also apply to the movement of characters arms and legs, or anything that moves around a pivot.  I had to do this exercise three times to find the right timing.

First Try

Here I purposely didn't follow the timing chart Brian provided in his book.  He timed the action on twos, meaning he broke the motion down to take 12 frames to swing left to right, then doubled each frame to make 24 frames, or one full second.  I thought if I did it on ones, a new drawing for each frame, I would have to figure out my own timing, which would force me to think things through more and understand things better.  As you can see, the way I broke it down the pendulum tends to favor the two extremes for too long.  It seem to hover, defying gravity, at the end of each swing.  So that was no good.

Second Try

So here I went back and followed Brian's timing chart exactly, hoping to discover what I did wrong.  While it did help me figure out where the timing was wrong, I wasn't exactly happy with his timing either.  While the timing of the slo-in and slo-out feel right, the speed of the pendulum through the middle part of the motion feels too quick.  Also note the more jerky aspect to the motion.  Thats a result of animating on twos.

Third Times the Charm
(You are getting sleepy…very sleepy…)

Using the previous two tries, I found a way to breakdown the motion to have the right timing for the slo-in and outs and not speed through the rest of the swing.  Instead of having the pendulum continuously pick up speed through the downward movement of the swing, I had it pick up speed, then maintain a certain speed through the majority of the swing.  Then I just had the slo-in and slo-out at the very beginning and end of the motion.