  In this paper the Bagley-Torvik Equation is considered with the order of the
damping term allowed to range between one and two. The solution is found to be
representable as a convolution of trigonometric and exponential functions with
the driving force. The properties of the effective decay rate and the
oscillation frequency with respect to the order of the fractional damping are
also studied. It is found that the effective decay rate and oscillation
frequency have a complex dependency on the order of the derivative of the
damping term and exhibit properties one might expect of a thermodynamic
Equation of state: critical point, phase change, and lambda transition.
