What causes the pendulum to seems out of balance?

Check that the hands are tight and also that they are not touching. and jamming. Remove the battery and replace it. Some have a lever to give it a jolt to get moving.

https://www.google.com/search?q=Infinity+group+Pendulum+Wall+Clock

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If your wall clock is running but the pendulum is not swinging, it may be due to a few potential issues with the pendulum mechanism. Here are some steps you can take to repair the pendulum mechanism:

1. Check the suspension spring: The suspension spring is a thin strip of metal that hangs down from the top of the clock and holds the pendulum in place. Check to see if the suspension spring is properly attached to the clock and if it is straight. If it is bent or damaged, it may need to be replaced.
2. Check the pendulum leader: The pendulum leader is the part of the clock that connects the pendulum to the clock's movement. Make sure that the pendulum leader is properly attached to the clock and that it is not bent or damaged.
3. Check the escapement: The escapement is the part of the clock that controls the swing of the pendulum. Make sure that the escapement is properly lubricated and that it is not damaged or jammed. If it is damaged or worn, it may need to be replaced.
4. Check the beat setting: The beat setting is the adjustment that ensures that the pendulum swings evenly. Make sure that the beat setting is properly adjusted by moving the pendulum to the left or right until it swings evenly.
5. Check the weights: If your clock has weights, make sure that they are properly attached and that they are not obstructed or damaged.

If you've tried these steps and the pendulum still isn't swinging, it may be best to contact a professional clock repair technician for further assistance. They will have the expertise and tools needed to properly diagnose and repair any issues with your clock's pendulum mechanism.

It is a handsome longcase clock and rather elaborate - it would be disappointing to discover the weights and pendulum are merely decorative.

I have only encountered one similar clock and it had one battery to keep the pendulum swinging and another to power the clock. The battery had to be fairly fresh or the pendulum stopped swinging. The clock also had to be level or the pendulum stopped.

If you took the picture when the pendulum was stationary, the clock appears not to be standing vertically. It is important they stand vertically in both planes to the nth degree.
There is also a fable about a clock never being happy standing next to or hanging on an exterior wall, sometimes not such a fable...

I don't think the pendulum is the problem. I suggest you should level the clock (considering the shape of the case a plumbline would be best), fit a new battery and give the pendulum a swing - if it doesn't keep swinging, there is probably a fault with the motor.

They were all important once, until about 1930, but are no longer used for precise timekeeping, just decoration.

The property of a pendulum which made it so is that, for a frictionless pivot and a massless rod with a relatively massive bob on the end, the swing period depends only on the length of the pendulum. Thus designs focussed on those factors.

In practice even the expansion of metal parts due to the heat of the day caused errors, and they could not be used in vehicles or boats. The search went on.

If you have the patience, you could try the following.
Set the pendulum in motion - this will slowly wind down the mainspring. The clock will probably stop after a few seconds. Set the pendulum swinging again as necessary, and if you're lucky the period that it ticks for will increase each time.
You will need to be patient and persevere - what you are doing is very gently releasing the tension on the mainspring.
This is not guaranteed to resolve the problem, but it won't harm the clock or your bank balance to try. Failing that, there is a mechanical fault that is causing it not to wind and you are strongly advised to place it in the hands of a reputable and competent clock repairer.

I have a clock with a pendulum and it has two batteries, one for the clock and one for the pendulum.

Perhaps your is the same?

Everybody should know that the coaster clocks discussed here run on batteries. The timing mechanisms, the chimes as well as the pendulum all are powered by a battery. Changing the speed of the pendulum is impossible because there is no adjustment. Besides, it wouldn't matter anyway. The pendulum has now affect on the clock's ability to keep accurate time. It is purely aesthetic. This is a pretty cool looking clock and even has weights, but those are also purely aesthetic and do not move the way a classic grandfather clock weight would move. The moments with these clocks are not designed to be worked on. These clocks are relatively inexpensive (approximately $300) but do add a nice look to your home. Grandfather clocks snobs would say though; this is not a true timepiece. They're right... Sorry.

This could be for too many reasons. It will not be possible to fix this without taking it to a qualified watch repairer who will be able to take a look and determine the exact fault.

It could be a blockage in the train of wheels.
It could be a broken balance staff or mal-adjusted balance spring.
May be broken palets or mainspring - the list goes on and on.

Find a local trustworthy watch repairer and they will give you a free estimate in most cases.

Best of luck.

CLOCK OILING TIPS * NOTE: Many Master Clock Smiths and Hobbyists used many different oils and as many different techniques.
* It is only good sense to use only the best in quality when selecting clock oils and grease. A number of fine oils are made especially for clocks. The oil used should stay in place and not evaporate easily and have no tendency to gum or get sticky as it ages. Most clock oils meet these standards. [CAUTION: Never consider using non-clock lubricants, as they tend to not really work well in clocks. Some are too light and cause unnecessary bushings wear, while others are too thick or can evaporate, over time will gum up and stop the clock prematurely.]

Oiling Procedures
-Main-springs are oiled after cleaning and before they are recoiled.
-Teeth and pinions are never oiled.
-Normally, the dial train of gears, hour wheel, minute wheel and minute wheel post are not oiled. However, oil is used between the center shaft and cannon pinion where slip friction is present in setting the hands.
-All points of friction such as train wheel pivots to bushings are oiled. Verge faces are oiled directly.
-Oil is always used sparingly and should never run all over the plates.

Hope this tip helps.

R/
DAvid

http://antiqueclock.clockstop.com/oil.htm