thanks, I was doing good until the words " signal analysis" popped up.;D
Sorry. I did not mean to muddy the waters. Electronic equipment can be very complex, or very simple. I don't know your background, or how familiar you are with electronic components. It is very difficult to communicate a troubleshooting approach over the internet, phone, etc. to another experienced tech, let alone a novice. And frankly, I wasn't offering to do long distance troubleshooting for you, because my time is also valuable. I spent many years learning my trade. I was merely trying to say there are usually things you can check yourself before you involve a tech or repair service.
For the record, "Signal Analysis" usually involves injecting a signal (or signals), and looking at the output (with a O-scope, DMM, spectrum analyzer, etc.) You can do a lot of troubleshooting before you get to that stage. Generally, with any electronic circuitry, you have inputs and outputs. The inputs might be switches, pots (like the volume controls on old audio equipment) or sensors. They might also be a digital signal from a control panel. Outputs might be digital readouts, drive motors, electromagnets, and valves for air cylinders. If you have a sense for how the circuit is supposed to act while it is functioning correctly, that often helps you narrow the problem down. For instance, if the motor isn't running, you can trace the motor wiring back to the board, to see if you have a loose connector or connector pins. Was there any smoke before the board failed? Look for burn marks on components, especially relays, power transistors, etc.. Are LED's and light bulbs supposed to be lit when the circuit is on? You might not have any power to the circuit. Look for a power supply (wall transformer, brick, open frame supply) Is a fuse on the supply blown? Sometimes you can substitute another component, like wall transformer to see if that is the issue. If a switch is dirty, and not making contact, cleaning it with switch contact cleaner might do the trick. If you look at the backside of the circuit board and see a solder connection that is grey, or an obvious loose connection or broken wire, all you might need is some solder and a soldering iron.
Much of today's computerized equipment does not have mechanical switches, pots, and etc. That makes it much harder to troubleshoot. (In my opinion.)
I am not familiar with pendulum clocks, but I assume the pendulum regulates the clock speed. I would start with a thorough search to learn the operating principles of an electromechanical pendulum clock. I'm guessing an electromagnet (or solenoid) is pulsing (attracting) the pendulum at a precise time determined by an optical sensor. If, for instance, you blocked the sensor, and put a screwdriver blade near the electromagnet, you would know if it is operating.
That's all the advice I have for you right now. Best advice is to find out how the equipment is SUPPOSED to operate.