We present new results on oscillations of the K1.5 III giant Arcturus ( \alpha Boo ) , from analysis of just over 2.5 yr of precise photometric observations made by the Solar Mass Ejection Imager ( SMEI ) on board the Coriolis satellite . A strong mode of oscillation is uncovered by the analysis , having frequency 3.51 \pm 0.03 \mu Hz . By fitting its mode peak , we are able offer a highly constrained direct estimate of the damping time ( \tau = 24 \pm 1 d ) . The data also hint at the possible presence of several radial-mode overtones , and maybe some non-radial modes . We are also able to measure the properties of the granulation on the star , with the characteristic timescale for the granulation estimated to be \sim 0.50 \pm 0.05 d .