This paper derives the dynamic equations for a dumbbell-shaped spacecraft equipped with control moment gyroscopes. Using the theory of gyroscopic flexible bodies, a modal analysis is conducted on the constrained boundary of the dumbbell-shaped spacecraft, leading to the determination of its natural frequencies and mode shapes. Zero-input response analyses are conducted for both the constrained-boundary spacecraft and a cantilever beam model, under two conditions: with and without damping. The results are then thoroughly analyzed. A comparison between the direct method and the modal superposition method shows that truncating after the fifth mode yields higher accuracy. This research provides a foundation for further studies on free-boundary modal analysis of dumbbell-shaped spacecraft and the optimization of control moment gyroscope installation positions.