Pendulum does not move

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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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.

It sounds like the drive spring might be worn. A Good clock and watch specialist will be able to overhaul and service the clock for you. It might cost you a bit more money but if it is a family clock it could be worth it.

probably find that the clock has it's own aa battery
the pendulum has it's own aa battery and the chimes have 2 aa batteries

When was the last time it was serviced? The movement probably needs a good cleaning and/or oiling.
UsedClockParts.com

Hi Pam,
I have a Howard Miller Grandfather clock and the pendulum swings very slowly and from far left to far right travels only about three inches at best. It doesn't need to move any more than that to make the "Verge" move the "Escape Wheel" to rotate the gears to keep the hands moving at the correct tick.
Howard Miller Grandfather Clock

Hi Pam,
I have a Howard Miller Grandfather clock and the pendulum swings very slowly and from far left to far right travels only about three inches at best. It doesn't need to move any more than that to make the "Verge" move the "Escape Wheel" to rotate the gears to keep the hands moving at the correct tick. Howard Miller Grandfather Clock

Clock may either need to be decked out from the wall at the top, or pushed all the way up against the wall. These clocks have inexpensive quartz movements that aren't of the highest quality. If the clock is more than a few years old, it may be that the electromagnet that impulses the pendulum back and forth has just expired. You might try Clockit.com, or maybe Timesavers.com to find a replacement movement. Hope this helps, Good Luck

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.

Give the pendulum a shove and do it every time you pass the clock. I got mine going from swinging for just 20 seconds to working permanently, at least until the next battery change.