The OM-1, OM-1 MD, OM-1N, OM-2 and OM-2N all have focal plane shutters as well as a PC type flash sync socket. As you are looking at the front of the camera, the PC socket is on the right hand side of the lens mount at the same level as the carry strap lug. As part of the PC socket, there is a switch labeled "X" (in blue) and "FP" (in black). You will notice that the shutter speeds 1 second through 1/60th second on the shutter speed dial are in blue and the speeds 1/125th second through 1/1000th second are in black.
The shutter is composed of two separate curtains. The film is exposed to light by the first curtain moving out of the way of the film gate and then the second curtain moving to cover the film gate up to complete the cycle. When you advance the film, the shutter is reset to the original configuration. The shutter curtains are small and light, but they still have some mass and they still must travel about 1.5 cm. The travel takes time. To get a shutter speed faster than 1/60th second, the first curtain will start moving and before it completes it's travel, the second curtain starts to move. The result is an open slit that moves across the film gate. So at shutter speeds 1/125th through 1/1000th second, the whole frame is not exposed at he same instant.
Now we know how the shutter works and we can consider the problem of synchronizing the shutter with a flash system. Electronic flash has some desirable qualities. Color temperature is the same as daylight. The "flash" is extremely bright, but extremely short in duration. The problem with higher shutter speeds is that the Flash of electronic flash is so short that the slit moving across the shutter will only expose a small area of film (less than the whole frame) before the "Flash" is over.
In the 1970's and earlier times flashbulbs were available to photographers. There were several different types of flashbulbs including type F (fast peak), type M (medium peak) and type FP (focal plane). Flash bulbs are simply a glass bulb filled with oxygen and a metal mesh that burns and produces heat and light. Type FP flash bulbs were made to burn for a long enough time that they can be used with cameras that use a focal plane shutter. For example, Sylvania FP26 flash bulbs can be used to synchronize with any shutter speed of your OM-1 up to 1/1000th second.
If you have an electronic flash with a PC cord connection, plug the cord into the PC socket of the camera. Set the PC synch switch to "X" (in blue) and use any of the blue shutter speeds on the camera (1 second through 1/60th second. You can also use type "M" or type "F" flash bulbs with the "X" setting provide you use 1/15th second or slower. You can use type FP flashbulbs at any shutter speed.
It is interesting to note that Olympus developed the OM-4T and the F280 electronic flash to mimic the focal plane flash system. the F280 flash uses a series of flash pulses to get a long duration burst of light.