Abstract: An "isoharmonic" sports bat, for example a baseball bat or cricket bat, includes a hitting surface for impact with a ball, wherein the duration of a half cycle of a selected mode of vibration of the hitting surface when in contact with the ball is approximately equal to the contact time between the hitting surface and the ball during an average impact. This allows the vibrational energy of the bat to be returned efficiently to the ball, which improves the coefficient of restitution, and the peak contact force between the bat and the ball may be reduced. The hitting surface may be formed by a plate attached to the bat.