Our design challenge was to develop a skyhook system with a pneumatic actuator and spring so that the Scan Eagle unmanned system can be captured after flight. This report contains information that defines the motion of the UAV as it approaches the skyhook using dynamic and vibration analysis. The initial tension, damping coefficient, and spring constants for the cable, actuator, and spring were designed so that the unmanned system may be captured by the skyhook and minimize the total cable force on the unmanned system. In order to do this, an equation of motion was derived to model the system graphically through a computer simulation. Once the equation is derived, it can be plotted in Matlab to demonstrate the position and velocity of the unmanned system after it is captured. This process and simulation are demonstrated in the following report.