A flowmeter includes a vibratable flowtube that has internal damping characteristics that substantially result in a desired dynamic response of the vibratable tube to a change in a flow of fluid through the vibratable flowtube. The dynamic response may be to a change in a property of the flow of fluid, a step change in the flow, and/or a change in the mass flow rate. The vibratable flowtube may have frequency-dependent internal damping characteristics such that damping of a driven mode of vibration is not substantially increased and damping at one or more modes other than the driven mode are substantially increased.