In this work, we present a novel actuation strategy for a suspended aerial platform. By utilizing an underactuation approach, we demonstrate the successful oscillation damping of the proposed platform, modeled as a spherical double pendulum. A state estimator is designed in order to obtain the deflection angles of the platform, which uses only onboard IMU measurements. The state estimator is an extended Kalman filter (EKF) with intermittent measurements obtained at different frequencies. An optimal state feedback controller and a PD+ controller are designed in order to dampen the oscillations of the platform in the joint space and task space respectively. The proposed underactuated platform is found to be more energy-efficient than an omnidirectional platform and requires fewer actuators. The effectiveness of our proposed system is validated using both simulations and experimental studies.