"The Pit And The Pendulum" is not only a popular Poe title but describes one of the key issues facing pool and billiards players. I have to spend a lot of time deconstructing the old teaching (okay, still currently being taught) that claims a pool player wants a smooth, pendulum stroke to play their best.

Baloney! A pendulum-like stroke is far closer to the mark.

In other words, their is a continual stream of pool teaching which describes an excellent and classic pool stroke as shown step-by-step on this GuideSite as a pendulum motion.

All that is otherwise accomplished is the pool player is set backwards.

Edgar Allen Poe's The Pit And The Pendulum (remember the short story of horror and its movie adaptations?) describes what this billiards teacher feels when the common instruction "the perfect pool stroke is a pendulum movement with the shooting arm."

As Poe wrote, "I WAS SICK-sick unto death with that long agony; and when they at length unbound me, and I was permitted to sit, I felt that my senses were leaving me..."
These three points below will help your stroke tremendously...
Here's the problems I'd cite, the "pit caused by the pendulum":
1.A pro's pool stroke is not a true pendulum but has an elongated straight line motion.
Pretend your pool stroke is a perfect pendulum arc. Where must you strike the cue ball along the arc of the forward stroke? That's right. Problem #1 is unless you strike the cue ball at the precise bottom of the arc, the cue tip must be rising up vertically or headed downward vertically at impact.

Repeat, unless you hit at the precise bottom of the pendulum, that is, perfectly return the tip to the bottom of the arc you began with the final backstroke, you miss your aim point on the cue ball. An aimed center ball hit will have unwanted topspin or draw spin.
The best players work their wrists, forearm and yes, even their upper arm, to elongate slightly the bottom of the arc, to straighten it. Just as in golf, an arc with a shallow or straight curve near impact sends the ball flying straight ahead.
Application against Problem #1: Forget making a perfect pendulum and stroke freely. It will be similar to, but not exactly, a pendulum movement, if your shooting hand, wrist, and entire arm are allowed to relax during the practice strokes and final stroke. Eliminate the tension in a stroke caused by forcing perfect arcs through the air.
More About Correct Arm And Wrist Motion In The Stroke

2.The notion of pendulum timing throws off true pool stroke timing.
The simplest way I explain this to my pool students is this--many billiards strokes require an accelerating forward stroke, so trying to do a perfect 1-2, 1-2, 1-2 timing on back and forward strokes, be they practice or actual strokes, is usually wrong and hampers the final stroke.
Think about it, the beautifully timed pendulum arc of say, a grandfather clock, can't occur in a pool stroke because the cue stick hits a ball near the bottom of the arc going forward.
Application against Problem #2: Forget timing your stroke consciously as a perfect one-two backstroke-forward stroke. Let the cue stick come forward fluidly and quickly through the forward stroke instead (and a correct pro grip will help you here greatly to create a fluid, accelerating stroke--when you need it--or a softer, slower stroke when you don't.
A Practical Help For The Correct Grip On A Super-Powered Draw Stroke

3.A pendulum stops at either end of its arc, nothing like a pool stroke.
The most subtle trouble with making a true pendulum pool stroke has to do with the Newtonian physical facts of arc movement--remembering Galileo's observations as the pendulum comes to a complete stop at either end of its arc.
All coming to a complete stop on the backstroke will do for a player is change the feel of the weight of the cue in their hand and throw their timing off.

Application against Problem #3: Relax through both ends of the stroke, backwards and forwards, realizing that if you don't stop at the end of the backstroke, you will be building momentum to accelerate on the forward stroke, which means cue tip momentum comes through the cue ball perfectly to give it optimum roll or motion going forward. An accelerating stroke, a straight stroke.

Note that it seems like certain pros stop on their final backstroke. In reality they slow each successive practice stroke down, slowing, slowing, slowing until it seems--it's a real close thing if you watch the pros closely--as though they stop. It's truly an almost imperceptible stoppage of movement.
*** Take my three tips above and you won't feel as I do when I listen to the teachers pushing the pendulum method on their books and websites... as Poe put it in The Pit And The Pendulum:
The sentence-the dread sentence of death-was the last of distinct accentuation which reached my ears. After that, the sound of the inquisitorial voices seemed merged in one dreamy indeterminate hum.