I am in a class and a fellow student wants to put a long pendulum on a movement from shorter case (longer case is nicer and has a window at the bottom to show pendulum). From looking at the "everything you ever wanted to know about pendulum" posting here, https://mb.nawcc.org/showthread.php?114670-All-about-pendulums&highlight=everything+you+wanted+to+know+about+pendulums I understood that a compound pendulum will allow someone to "lengthen" a pendulum's effective length to act as if it were longer (and work slower) than its physical length. In other words I can see how a compound pendulum can make a short pendulum act longer - but I don't see how I can make a long pendulum 'act shorter' .... If she just puts the long one on I assume it will drastically slow down the clock (I am talking about doubling or tripling the length of the current pendulum). Any ideas? Maybe make pendulum heaver at top half and lighter on bottom half with a very light bob? What about one of those pendulum's that have branches that go out to the left and right of the main pendulum assembly?

In order to make a pendulum act shorter i.e. swing faster, you must raise the center of oscillation. If the short pendulum was originally long enough, you might add weight higher up the pendulum just below the movement. You might also put buffer springs high in the case that the pendulum would bank against to shorten its arc. A third alternative would be to put a linkage in the pendulum so that the top half could swing and be impulsed while the bottom half just pretended. I think there are really good reasons why none of these things are done in serious clocks.

Simplest way is "top loading" --adding mass to the stick above the bob. See All About Pendulums entries #3 and #7.

This question really depends a lot on how much longer does the pendulum need to be? Top loading has some serious limitations in effect. If we're talking about several inches, I'd consider a EW switch to one with fewer teeth, or doing the same thing with another wheel in the train.

I didn't see the part about "doubling or tripling the length". Ain't gonna do that with top-loading. Either get into swapping out gears, as Shutt suggests, or go for a compound pendulum if there's enough room in the top of the case. Again. see All About Pendulums

Place a light shell for the pendulum fake bob and then put a heavier weight higher on the rod. It might be simpler to use a escapement wheel with less teeth and just use a longer pendulum. Using a fake bob will still swing as fast as it did before. A long rod with the fake bob swinging fast would not be pleasing to look at. Tinker Dwight

Well, in as much as the movement does not belong to the case, the most practical thing may be to simply locate another movement that is already setup for a long pendulum. To get the short pendulum movement to keep time with a pendulum two or three times longer will likely require an escape wheel change and at least one wheel/pinion change. It can be done but changing wheels usually involves relocating pivot holes and a bunch of work. RC

"Doubling or tripling" might require more than just changing the escape wheel. Might be a good idea to see if the movement you have was available in the pendulum length you need, then research to see exactly how it was done. Note, it is difficult to make a change in pendulum length that turns out exactly like you want. So a realistic plan would be to get it close and then do it again to get it like you want. Willie x

If you know the period of the clock, you can calculate the various options. If you have an empty pendulum bob shell, we can do some measurements of weights and calculate the location and weight of a bob that might work. You want to make the shell and rod as light as possible. It would be fun to calculate this one. As RC says, changing the escapement enough to lengthen it would likely require drilling new bushing holes. What is the difference in length you are trying to achieve? Tinker Dwight

If the movement requires (say) a 6-inch pendulum, and the case calls for a 12-inch or 19-inch pendulum, you have a serious mis-match that can't be cured by fiddling with the pendulum. You'll have to rebuild the going train, as others have suggested. Or get a different movement for the case. Or get a different case for the movement. Is what I think. ......... Actually, I think something else. Start with your 6" pendulum. Fabricate a mock extension out of the lightest possible material (maybe balsa stick and alum. foil bob). Attach it to the bottom of the pendulum rod. The small amount of added mass will slow the clock down. Move the real bob up on its sick enough to counteract that mass. That should work. Course it would probly be ugly as sin.

The moon is closer and it's surface gravity is less than on Mars, so it would work better on the moon. Raising the center of oscillation of the longer pendulum to equal that of the shorter pendulum would work on Earth, but a problem might be the width of the longer case. At twice the original pendulum's length, the longer pendulum's arc would be twice that of the shorter pendulum, and might strike the walls of the case.

Good answers above. I guess the correct term in clocks is "center of oscillation". I think this is the center of gravity. To determine the center of gravity of the old pendulum you need to get it to balance on a sharp edge, like a knife. Measure the distance to the point the pendulum attaches. When you make your new longer pendulum adjust it by adding or removing weight so that it balances at almost exactly the same distance as the old pendulum. The bad news - the important distance is from the pendulum's pivot point...not its attachment point. If you make the new pendulum the same weight with the same center of gravity...perfect. If you can't, you may want to remove the component that actually attaches to the pivot point and include it in a calculation....you will now need to use some mathmatics to combine centers of gravity. If you want, I'll crack out an old physics book and get you an equation to use.

If the component above the pendulum that attaches to the pivot is of low mass compared to the pendulum, you should be able to adjust with the device you hopefully are adding to the new pendulum...a nut or other weight that can be moved up or down the pendulum for finer adjustment.

I've been thinking about what Bangster suggested above. It might be possible to construct a pendulum stick with two bobs. The upper heavy bob (probably heavier than the original) would need to be adjustable. The lower one would not have to be, and should be constructed of the lightest possible material (maybe a paper bob). The stick below the upper bob should also be as light as possible, perhaps narrower and thinner than the upper part. Then you could likely adjust the upper bob high enough to compensate for the added material below it. It would swing as fast as the shorter pendulum though. It would be interesting to experiment with it.

Well, it is not the center of gravity. If it were, life would be easy. To be technically correct, you need to determine not only the center of mass but also the moment of inertia about the center of swing ( fulcrum or 1/2 suspension spring ). You find the center of mass for each component and multiply the distance of the center of mass times each mass and sum those up. Call that B. Next you take the center of mass of each part and multiply that times the length squared. Add those together. Now take each masses moment of inertial and add that to the sum. Call that A. To be accurate, you need to include everything, rod and bobs. Take 2*Pi* sqroot( A/(B*g)) = period of full cycle. g is the gravitational constant that is consistent with the mass and distance measurements used. Now, wasn't that easy? Tinker Dwight

I was trying to keep things simple for this simple harmonic oscillator. The equation will simplify to T = 2*pi*sqrt(L/g), where T is the period of motion, L the distance to the center of mass, and g the force due to gravity, if all of the mass is concentrated at the center of mass (or gravity...assuming a uniform gravitational field). It actually gets a bit more complicated...geometries come into play when calculating the moment of inertia about the pivot point. Tinker, I must ask, do you believe the geometries may come into play enough that my approach would not be the easiest approach? Hope to work with you one day on making a clock with an inverted pendulum...I think we need controls for that one....no bumbers allowed!!!

Tink is no doubt right. But I'm not sure that the equations are as useful (for current purposes) as the empirics that Shutt and I have talked about. Start with an accurate pendulum. Add small mass below sufficient to satisfy appearances. Adjust main bob upwards to deal with the added mass. Is what I think.

Bangster, Tink is right. It is the moment of inertia about the pivot. If modeled like a weight on a string it simplifies to center of mass. If a light bob is used (paper, styrofoam, etc.), and the mass is concentrated at the old location, as you and Shutt suggested, I think you have the easiest and best approach. By trying to get center of mass at the same location initially it should reduce the trial and error testing needed. It is simple to find the cenetr of mass. It's been a lifetime since I calculated a moment of inertia. I think it better suited for some designer using FEA software for something to be mass-produced.

As long as all the weight is in one spot, one can often ignore all the moments of inertia that effect things. Once you start having separate weights you have to start calculating each parts contribution separately. Even a large diameter, heavy, bob can slow a pendulum because the bob's rotational moment adds to the equation, even though its swinging inertial is compensated by the CG. You want to use as light a bob as you can higher up because its rotational inertial adds a higher percentage as it gets closer to the suspension. Each piece adds two moments of inertial. One is from the lever arm and the other is its rotational inertial. Anyway, once you use the simple equation, you know that things will add, causing the pendulum to swing even slower then the estimate. Also, with the longer fake pendulum, there will be more air drag. That may mean that you'll need more drive. That you won't know until you try it. Good luck Tinker Dwight

I'm not following you here, tinker. The higher bob (in the example we've been talking about with two 'bobs') must be the heavier one.

I'm sorry, I didn't finish my thought, It is a balancing act. It has to be heavy enough to make the false pendulum part seem light but if too heavy, it will be big in diameter, causing it to have more rotational inertial. This will require it to be even higher up the pendulum to compensate. Then the lever part of the inertia will have less effect compared to the false pendulum part. Eventually, it becomes a losing battle. Too much rotational inertia without the help of gravity. It goes back to keeping the false part as light as possible or even a very heavy bob, higher up, won't speed it up. The simple pendulum equation doesn't include the rotational inertial component of the bob ( It is generally ignored ). As you bring the bob closer to the suspension to speed the pendulum up, it increases as a percentage of the timing effect to the point that it actually slows the pendulum as you raise it. It all depends on how heavy the false part is. When you reach the height, of the upper bob, that it switches from slowing the pendulum in both directions, it will be ineffective to move it much to regulate the speed. Still, yes, you are right it has to be heavier but there is a point of no return where no matter how heavy, you can't speed it up. Tinker Dwight

In other words... Moving the bob up moves it closer to the center of rotation, making clock run faster. When it is exactly centered on the center of rotation, that's as fast as it can go. Raising it further will have the opposite effect, making the clock run slower. A heavier bob will start out closer to the center of rotation than a lighter one, giving it less room to travel up effectively before reversing. Is what I think.

I thought some viewing this thread might appreciate putting this discussion into a bit more digestible version of what is at play.... A simple pendulum, think of it as a weight suspended from a very light string and attached to a rigid point that does not move, can easily be analyzed and its movement predicted by knowing only the length of the string. It does not matter how heavy the weight is, its rate of swing is determined only by the length of string....make the string longer and the pendulum slows down...make it shorter and it speeds up. A physical pendulum can sometimes be approximated as a simple pendulum, if the bob is a concentrated weight significantly more massive than the very light rod that attaches it to the pivot point....move the weight up the rod and the frequency increases, lower the weight and the frequency decreases. The moment of inertia is at play in even the simple pendulum...it just can be simplified. How does moment of inertia become important? Looking at the simple pendulum, may make it clear what is at play....In the simple pendulum the center of mass is accelerating at the rate driven by gravity...like the rate a rock would fall if dropped off a building, but in fact if you look at the pendulum some parts are moving faster or slower than what gravity would have them fall at. Take the end of the bob farther from the pivot. It is moving faster than than the center of the bob....you can think of that part of the bob as trying to slow the pendulum down. On the other side of the bob's center of mass it is going slower than at the center, you can think of it as trying to speed up the pendulum. In this modified pendulum that is being attempted, it truly is not a simple pendulum and its rate will be dictated by what is called the moment of inertia about the pivot or fixed point. For simple shapes there are equations developed from calculus to determine the moment of inertia. The shapes have to have uniform density. If densities and dimensions of these simple shapes are known, you can easily calculate the rate or period of swing by combining the moments of inertia of each of the components. Takes a lot of work, IMO. In fact pendulums are often used to calculate the moment of inertia when those geometries get hairy...It is far easier to measure the moment of inertia than it is to calculate....unless you have FEA (Finite Element Analysis) software at your disposal....you still need to know the desities of the materials when using the software. The ideas suggested above will make a trial and error approach far easier...keep the lower bob and rod light (paper) as suggested and the upper bob make massive...(more so than the original) and slightly higher up than the original arrangement to compensate for the additional fake bob below. I think I would be using styrofoam for that bob and lower rod and with the thinnest layer of paint possible.

I can't remember if it was asked, but I do wonder one thing. The plan is to double or even triple the length of the original pendulum. If this pendulum is swinging at the same weight as the original, how unnatural will its movement appear? Will it be noticable or objectionable?

"moment of inertia" = "center of oscillation" No? By definition, a "simple pendulum" is one that has no mass below the bob(nor above): no rating nut, no stick extension, nothing. So, no pendulum with an adjustable bob is a "simple pendulum". Let's call a pendulum with mass both below and above the bob, as in most clocks, an "ordinary pendulum". An ordinary pendulum doesn't consist of a massive bob and a massless string. It consists of the entire assembly below the suspension point: bob, stick, anything else that's attached:maybe some mass below the bob, maybe some mass above the bob. The whole thing is the pendulum. The mass of the whole thing is relevant. How the center of mass is located with respect to the assembly is relevant. The one we are considering, with the ultralight extension, is an ordinary pendulum. It has mass on both sides of its center of gravity (as well as center of oscillation). The added mass of the extension slightly lowers its center of mass. You can offset that by shifting mass upward (up to a certain point). The bulk of its mass is in the upper "working" bob. The fact that there is significant (but small) mass below the bob doesn't change the basic behavior of an ordinary pendulum: move heavy bob up, clock runs faster (to put it as simply as possible). Is what I think.

No Bang Moment of inertia is like how hard it is to rotate the item about the pivot point. There really isn't a center of oscillation. The moment of inertia doesn't care where around the pivot, it is, only how far away it is radially and the mass. If you were to put a one pound weight on the end of a rod 1 foot long and mounted it so that it rotated without gravity playing a part, Swinging it sideways at some rated back and forth would take 1/4 the force then if it were 2 feet long. Gravity does care where the center of gravity is because that is where it pulls. As for Visteo's point about the end of the bob swinging faster than the top, it is possible to break the inertia of the bob into two parts. The first part assumes that the bob is mounted such that there was a pivot at the center of gravity of the bob. This inertia is just the length squared time the mass ( what is assumed for a simple pendulum ). The second part is the rotation of the bob. It can be calculated for simple uniform shapes, as Visteo states but it is often easier to calculate from a pendulum method. These can then be simply added together for the total moment of inertia. My point was that we typically ignore the rotation of the bob to use the simple pendulum formula because this is such a small percentage of the total moment of inertia because both are related to a distance squared. One the length of the rod and the other the diameter of the bob. When moving the bob closer to the pivot, the rotational inertia of the bob becomes a larger portion of the rotational inertia. The simple point weight at the end of a string is no longer a good way to describe it. Also, depending on the ratio of the masses involved, once the upper bob cross a point that it is no longer increasing the pull of gravity ( because the pivot is supporting more of its weight, compared to it inertia ), moving the second weight up would actually be slowing the pendulum and not speeding it up. For a really light upper weight compared to the bob, that point along the rod would be at 1/2. For a heaviy upper weight, it is someplace closer to the the pivot. That turnaround point does no necessarily require a portion of the upper bob to cross over the pivot. It really depends on the ratio of the weights their moments of inertial about their on centers of gravity. All back to the point that one needs to keep the false pendulum as light as possible because it may not be practical to find a material for the upper bob that has a high enough density to keep from being at that point along the rod where moving the weight higher will increase the rate rather than decrease it. If to get it to run at the desired rate, requires one to have the upper weight at that point of reversal, the rate will be very insensitive to the bobs location, making it useless as a rate adjuster. Tinker Dwight

Yeah, I get it now: moment of inertia = rotational inertia. Ran into that terminology when I was working up my highly un-mathematized article "All About Pendulums". Then forgot about it. Tink supplied the formulas at the end of the article.

The problem isn't that a center of oscillation can't be calculated for any combination of two masses, it is that it does not continue to move up as the upper bob is moved closer to the pivot point. At some place along the rod, it will reverse and start slowing again. I know it is counter intuitive but that is because we are so used to think in terms of the simple pendulum. Where that point is is effected by the ratio of the masses and some significance of the rotational moment of the upper bob ( which increases in significance as it nears the pivot point ). Tinker Dwight

To demonstrate what I was talking about, I did some calculations. ( my computer with office is not working so I did it on my calculator ) Since I was doing it this way, I chose a pendulum with a with a 1 unit weight at length 1 long that produced a period of 1 unit time. ( I did this to remove the need to constantly include g, gravitational constant, and pi, for every calculation ). Since they are all constants, I can use whatever measurement system I find convenient. The period of my pendulum is just sqroot( 1 / 1 ) = 1. Which it the equation sqroot( M / G ) = T. M is the momentum about the pivot Sum( W*L^2 ) G is the pull of gravity on the weights Sum( W*L ) T being my arbitrary time measurement. L is the length to the weight. Now I add a 3 unit weight at 1/2 the length of the pendulum to make it run faster ( I'm assuming my weights are point sources or it would make thing a little slower from their rotational moments ). The equation becomes: SQROOT( / ((1 * 1 * 1) + (3 * 0.5 * 0.5) )/ ( (1 * 1) + (3 * 0.5)) ) = .837 for T First thing to notice that even though my center weight was 3 times heavier than the one at the end of the pendulum, being at half way only sped the pendulum up by about 20%. Now let make a table of the different locations for the 3 weight from 0.5 up to the the pivot. L , T 0.50 , .837 0.45 , .827 0.40 , .820 0.35 , .817 0.30 , .818 0.25 , .824 0.20 , .837 0.15 , .858 0.10 , .890 0.05 , .936 0.00 , .100 Notice that the pendulum was swinging faster ( T smaller ) until around 0.3 to 0.35. Then it started to swing slower again as the 3 weight approached the pivot point. So the weight that was 3 time as heavy as the weight at the end of the bob had its maximum effect at 1/3 of the length of the pendulum. Its greatest effect was only speeding the clock up by 22.5% So, I showed the inflection point of raising the center weight and the maximum effect of using a weight 3 time heavier than the bob was. What this shows is that you want the fake bob to be very, very, light. The inflection point is the ratio of the weights, the maximum speed up. Tinker Dwight