In helicopter design damping devices must be incorporated, because at specific angular velocities vibrations of the rotorblades can be reinforced by rotational-vibrational coupling, and build up catastrophically. Without the damping the vibrations will cause the rotorblades to break loose. The animation on the right provides a clearer view on the oscillation of the angular velocity. There is a close analogy with harmonic oscillation. When a harmonic oscillation is at its midpoint then all the energy of the system is kinetic energy. When the harmonic oscillation is at the points furthest away from the midpoint all the energy of the system is potential energy. The energy of the system is oscillating back and forth between kinetic energy and potential energy. In the animation with the two circling masses there is a back and forth oscillation of kinetic energy and potential energy. When the spring is at its maximal extension then the potential energy is largest, when the angular velocity is at its maximum the kinetic energy is at largest. With a real spring there is friction involved. With a real spring the vibration will be damped and the final situation will be that the masses circle each other at a constant distance, with a constant tension of the spring. This discussion applies the following simplifications: the spring itself is taken as being weightless, and the spring is taken as being a perfect spring; the restoring force increases in a linear way as the spring is stretched out. That is, the restoring force is exactly proportional to the distance to the center of rotation. A restoring force with this characteristic is called a harmonic force. The following parametric equation of the position as a function of time describes the motion of the circling masses:  The motion as a function of time can also be seen as a vector combination of two uniform circular motions. The parametric equations (1) and (2) can be rewritten as:  A transformation to a coordinate system that subtracts the overall circular motion leaves the "eccentricity" of the ellipse-shaped trajectory. the center of the eccentricity is located at a distance of formula_8 from the main center:  That is in fact what is seen in the second animation, in which the motion is mapped to a coordinate system that is rotating at a constant angular velocity. The angular velocity of the motion with respect to the rotating coordinate system is 2ω, twice the angular velocity of the overall motion. The spring is continuously doing work. More precisely, the spring is oscillating between doing positive work (increasing the weight's kinetic energy) and doing negative work (decreasing the weight's kinetic energy)  The centripetal force is a harmonic force.