WHAT ABOUT THE IDEA THAT THE WEIGHT HAS NOTHING TO DO WITH THE PERIOD OF A PENDULUM?
Well you can believe what you want. And if you are a physics major you may say that this is true. In theory you are correct. In clock repair not true at all. There are several reasons for this. First, the “center of gravity” of a pendulum determines its effective length as far as the clock is concerned. This has been determined by exaustive empirical study. So if you put a “different” weight on a pendulum the timekeeping will change. In other words if you change the pendulum bob you will probably change the timekeeping characteristics of the clock. It is important to understand here that if you “add” weight to a pendulum, you will change its effective center of gravity. To better understand this concept; think about it this way: How do you determine how long a pendulum is? Is it the pendulum rod, the suspension, the pendulum stick, or the pendulum bob? If you were doing a physics experiment, how would you make the pendulum shorter? You would probably shorten the string holding the weight. To adjust the timekeeping of a clock you move the bob up or down depending on whether or not it is running slow or fast. This changes the effective length of the pendulum, thereby changing the period. If you add weight to a clock pendulum, you will change the period of the pendulum and you will change the characteristic timekeeping of the clock, unless you add the weight in such a manner so as to NOT change the center of gravity, and you add enought power to the mainspring or or weight that supplies power to compensate EXACTLY for the weight you have added. Consider this: Lets say you have a wall clock that has a pendulum that produces one tick per second ( This is typical of many large wall clocks ). How many seconds in a day? 60 * 60 * 24 = 86,400. Now take that times 7 and you have 604,800 seconds in a week. In most repair situations and customer service situations, if a clock is more than 5 minutes a week off, you will get a call from your customer. This error is not acceptable to most people. Lets say you change the length of your pendulum so the period is one tenth of one percent slower that it should be on each swing. That is .001. One thousandth. Doesn’t seem like much? Better think again. 604,800 * .001 = 604 that is 604 seconds in a week. Depending on the gear ratio, the clock could be ten minutes off or more. Ok, lets say the error was only .0001 one ten thousandth. That would still be a minute a week. Annoying, but ok. However, lets say you had a 30 day clock ( there are clocks designed to run for 4 weeks on one winding ). That would be a half hour in a month. Probably not acceptable to most people. A tiny set screw on a small wall clock pendulum will make more difference than the .001. This does, as you can see, illustrate the fact that a heavier pendulum will be more accurate, because adding a small amount of “change of center of gravity” will have less overall effect on a heaver pendulum. Clock timkeeping error is additive in a way most people do not consider, and weight change on a clock pendulum does make a difference; sometimes a large difference. This theory mentioned above is precisely why clocks have been designed with temperature compensating pendulums, and suspension springs. If the temperature changes 10 degrees and the suspension rod expands say .01%, it will change the timekeeping. If the pendulum bob expands, and does so in a non-uniform way, the timekeeping will change, because the center of gravity will be altered by the changing shape of the pendulum bob.
Second: If you put a heavier weight(pendulum bob) on a pendulum the pendulum arc will decrease because you have not changed the amount of power that is pushing the pendulum yet you have added to the friction. With a shorter arc there will be less time between ticks. The escape wheel will move faster and the clock will run faster. Too much weight here and the clock will stop. This problem is worse with spring drive clocks than with weight drive clocks because of isochronal error. That is a fancy way of saying there is less power available from a mainspring when it unwinds. The reduction in power is not linear. Generally speaking the mathematics needed to design a clock was available many years ago. Most clocks have been designed well and the “stock” pendulums and mainsprings are crucial in providing good timekeeping. For this reason, I recommend when ever you can, keep the clock as original as possible. Unless you are a skilled mechanical engineer with years of experience in designing slow moving grear trains, you probably will not be able to improve much on the design of an old clock.
Third: If you put a lighter weight on a clock pendulum ( that is to say if you put a pendulum that is lighter on the clock ) the arc on the swing of the pendulum will increase slightly because you have reduced the amount of friction on the pendulum. Maybe I shouldn’t call it friction. As the weight of the pendulum increases it takes more energy to push it. As the weight of the pendulum decreases, it takes less energy to push it. Then there will be more time between ticks. The escape wheel will move more slowly and the clock will run slower. Remember that this effect is additive here; most clocks will tick hundreds of times in one day.
The strength of the suspension spring will also determine the arc of the pendulum. A thicker (stronger) suspension spring changes the arc , or swing of the pendulum ; it usually makes it shorter. Too thick (strong) and the clock will stop. Too thin (weak) and the clock will stop. A thinner (weaker) suspension spring changes the arc , it usually makes the pendulum arc increase. Remember, when the pendulum arc (swing) increases there is more time between ticks and the escape wheel turns more slowly which makes the clock run slower. All of these factors interact in a very complex way mathematically. Sometimes timekeeping is affected in ways that seem illogical at best. If a clock has an excess of power , sometimes you can get away with putting a stronger suspension spring on it. The key word here is sometimes. As soon as you start changing things you will need to be very careful. I strongly advise against changing a clock suspension spring or pendulum unless you use an exact replacement. If you have a clock that has no suspension or pendulum this may help you devise one by emprical study.