We study the time evolution of fast magnetosonic and Alfven waves in a coronal loop driven by random footpoint motions. The footpoint motions are assumed to be polarized normal to the magnetic flux surfaces in Linear ideal MHD. De Groof et al. (1998) (Paper I) showed that the input energy is mainly stored in the body modes when the fast waves are decoupled from the Alfven waves. Hence driving at the loop's feet forms a good basis for resonant absorption as heating mechanism.