why is my car's engine shaking?

Hello guys. So straight to the point - I just bought Honda Civic 2003 1.7 Diesel 74Kw, mechanical gear. Everything is perfect except for that shaking after a break from driving. I get to the car in the morning, turn on the engine and it's shaking like crazy when I stand still and more when I go back or forth at the very beginning, it stops shaking after I catch only few km/h speed. When I get to work, for some reason the shaking is gone in all of those situations. My friend says it must be a bad engine pillow (idk if that's what it's called in english, it's the part that holds the whole engine in place) but if that's the case, I just don't get why would it be the reason if it stops shaking after a 10km or so ride. via /r/cars http://ift.tt/2tBAtBx