This study presents a strategy for platoon formation and evolution of connected and autonomous vehicles (CAVs) for all traffic condition (stable and unstable traffic) and various vehicle composition based on a Spring-Mass-Damper (SMD) system. First, this study presents a strategy for platoon formation and evolution of connected and autonomous vehicles (CAVs) in free-flow traffic. CAV platoon formation and evolution are controlled by the spring constant and damping coefficient of the SMD system. Valid domains of these control parameters are derived based on physical vehicle properties (e.g., bounded acceleration/deceleration) for realistic control. The result suggests that the most efficient platooning can be achieved by the maximum relationship (where the spring constant is set at its maximum for given flow) between the spring constant and flow with critical-damping. However, the cubic relationship, coupled with over-damping, is more desirable in low flow states to allow more freedom for vehicles to cut in and out. Second, this study proposes the control method that aims to improve the platoon efficiency and stability after a cut-in movement (e.g., lane change and merging from on-ramp). The method seeks to resolve a disturbance created by a cut-in vehicle by systematically setting spring constant and damping coefficient based on the prevailing traffic condition. The control method is evaluated through simulation based on the changes of speed and spacing, recovery time to reach the desired speed, disturbance propagation, and platoon flow. The simulation result shows that the control method can effectively reduce the disturbance caused by a cut-in movement and improve platoon flow. Lastly, heterogeneous CAVs and mixed traffic of CAVs and manual vehicle are dealt as a way of extending this study. In case of the heterogeneous CAVs, based on their capabilities such as maximum acceleration and the desired time gap, the optimal order of CAVs that shown the best efficiency is found. For the mixed traffic, due to the different characteristics of CAVs and manual vehicles, the impact of CAVs on the manual vehicle occurs. Thus, this study proposes the range of the spring constant and damping coefficient to absorb the impact.