Molecular dynamics simulations are used to study mechanical energy dissipation in carbon nanotube oscillators of lengths of tens of nanometers. The principal source of friction is found to be the ends of the tubes and hence dynamical friction is virtually independent of the overlap area between tubes. As a result of this, tube commensuration does not lead to significantly increased frictional forces. The friction force is found to depend strongly and nonlinearly on the relative velocity of the tubes. It is suggested that a strong velocity dependence and strong contributions from surface edges may be quite general features of friction at the nanoscale.