What causes car to shake after starting then smooths out after 30 seconds or so?

It could be caused by any of a number of problems.

Some of the possibilities are:

* One or more worn sparkplugs that cannot deliver a hot enough spark. It may be providing enough spark to function after the engine warms up. * Low compression on one or more cylinder. Any cylinder with low compression will have a little more difficulty firing. * A sticking or plugged injector that has possibly flooded the engine when it was turned off or even not providing enough fuel at startup. * A sticking or poorly seated valve. * Oil fouled plugs. * Vacuum leak on one or more of the cylinders.