Time constant is important in control engineering applications. Is there any mathematical concepts that can be used to calculate time constant from system mathematical model?
Depends on your system. For instance, RC represents the time constant of an electrical RC circuit, for some flow system, it is mass (kg) / mass flow rate (kg/s).
That's a second order system and it should be related to damping and spring constants. Probably, if I recall correctly, Ogata book on control system has a nice description on how to determine different parameters of a second order dynamical system.