We study the excitation of MHD waves in a coronal loop as its field line footpoints are forced to follow the photo spheric convective motions. By focussing on the specific case of cylindrically symmetric footpoint motions, the original problem is reduced to one in which fast waves and Alfvén waves are decoupled. This allows for a full analytical treatment of the photo spheric excitation of both sausage waves and of torsional Alfvén waves. Previously, Berghmans & De Bruyne considered the case of torsional Alfvén waves. In the present paper we extend that analysis to sausage waves that are excited by radially polarized footpoint motions (e.g., typical for granules). The time-dependent solution that we obtain is written as a superposition of body and leaky eigenmodes whose excitation is easily determined from the imposed footpoint motion. This provides analytical insight into the dynamics and energetics of both impulsively and periodically driven sausage waves. In each case, we explain the time evolution of the generated waves and discuss typical "signatures" that can be looked for in numerical simulations and possibly in solar observations.