How are analog clocks synchronized? clocks on the frequency (50 Hz or 60 Hz) connected with power cable to the electricity network Those clocks that use a motor that runs exactly on the frequency (50 Hz or 60 Hz) and connected with power cable to the electricity network.
I mean - a frequency controlled clock / alarm - the frequency (50 Hz or 60 Hz) from the electricity network - those clocks that use a motor that runs exactly on the frequency ... with a number of gears ... a signal that moves the clock pointer hands (or flipping numbers). Like my own alarm clock also clocks in public spaces make use of it.
Those simple clocks do not have crystal oscillator 'quartz' ... do not have DCF77 ... do  not have GPS Time Signal Receiver. 
So, I mean NOT the atomic clock ... or NTP synchronized clock (computer / smartphone)... NOT a quartz-controlled clock / watch.
I mean then how the clocks - frequency controlled clock / alarm (with power cable to the electricity network) -  synchronize?
 A: Because so many different power generators are connected to the same mains circuit, it is extremely important that all generators maintain the same phase (and thus frequency) of the power supply. This makes the 50 Hz (or 60 Hz, depending on what continent you are on) a rather reliable reference signal.
In this website the question of mains power stability is examined. It turns out that in continental Europe there is indeed a deliberate effort to keep the long term average frequency at exactly 50.000 Hz, and when the accumulated error drifts too far (more than 20 seconds), a correction is scheduled where the generators will run at 50.010 Hz for a day, resulting in a 17 second "catch up" (1/5000th of 86,400 seconds). A nice graph from that website shows the phase error slowly increasing, then clearly dropping on day 41/42 and days 53/54/55 (presumably a correction took place there):

This leave the simpler question - how does a clock use the mains frequency to run stably? I once took an old alarm clock apart (how else do you learn stuff in the 70's - you weren't going to google it...) and discovered that there was a part that had a whole bunch of magnetic "teeth" of alternating polarity - 50 in total. Every oscillation of the mains voltage would advance this wheel by one tooth, so you would get two revolutions per second. This was then stepped down by some gears to give the hour, minute and second hand the right motion. And since "somebody" keeps the mean frequency constant, your clock never needs to be set... as long as you're OK with errors up to 30 seconds.
Of course if you take a 50 Hz clock to a 60 Hz country, it will run very, very fast. This is one case where an appliance really only works at the designed mains frequency.
I found the following diagram at http://sound.westhost.com/clocks/motor-f5.gif :

This shows roughly what I saw in my old alarm clock... Obviously one can choose the number of magnets and the gearing ratio so as to get sufficient torque and good time keeping.
