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Electric clocks generally have the hands, or the indicators of time in other form, driven by an electric motor.
If your Telechrone is old enough, the motor (which turns continuously 24 hours a day 7 days a week, all days of the month, etc.) may be getting old. Eventually such electric motors do develop a dry whine or rasp in their workings. This is owing to simple age and 'wearing out'. Such motors are sealed and have no lubrication points. You can tinker with it, try applying a little penetrating oil to the spindle near the seal that protects the interior of the motor (in case that seal is actually not airtight any more, and oil can get into it), but results are not at all guaranteed.
The motor may, eventually, have to be replaced... since that noise in the motor indicates increased friction, the clock may eventually run too slow to be usable, as a result, even aside from the noise.