Rotational–vibrational coupling

In physics, rotational–vibrational coupling occurs when the rotation frequency of a system is close to or identical to a natural frequency of internal vibration. The animation on the right shows ideal motion, with the force exerted by the spring and the distance from the center of rotation increasing together linearly with no friction.

In rotational-vibrational coupling, angular velocity oscillates. By pulling the circling masses closer together, the spring transfers its stored strain energy into the kinetic energy of the circling masses, increasing their angular velocity. The spring cannot bring the circling masses together, since the spring's pull weakens as the circling masses approach. At some point, the increasing angular velocity of the circling masses overcomes the pull of the spring, causing the circling masses to increasingly distance themselves. This increasingly strains the spring, strengthening its pull and causing the circling masses to transfer their kinetic energy into the spring's strain energy, thereby decreasing the circling masses' angular velocity. At some point, the pull of the spring overcomes the angular velocity of the circling masses, restarting the cycle.

In helicopter design, helicopters must incorporate damping devices, because at specific angular velocities, the rotorblade vibrations can reinforce themselves by rotational-vibrational coupling, and build up catastrophically. Without damping, these vibrations would cause the rotorblades to break loose.