Engine shaking violently usually happens when the engine is cold, and can be because the idle is too low (as corolla boy mentions) and/or it is not firing properly until things warm up.
Probably just needs a tune, new plugs leads etc, timing adjusted adn carb/injectors cleaned, as the fuel could be coming out in "gobs" instead of a fine spray.
Also mabey your choke/cold start injector or whatever your engine uses isnt working/ needs a clean