When my 2hp briggs & Stratton edger is running it suddenly squeals and vibrates and rejects the cord and stops the motor

Although you said rejected I assume you mean that the line is being pulled from the spool. Most line trimmers have a knife (really just a piece of metal) that trims the line to its maximum length. Knife is usually located on the edge of the underside of the cover. If the line gets to long it can wrap around an object and then be pulled from the spool.

Replace starter clutch