Radiation Damping in the Mechanical Oscillator

The typical model of the damped mechanical oscillator is the simple spring, fixed at one end, with a mass attached to the other. Air resistance is assumed to provide a retarding force which is proportional to the object's velocity. The equation of motion is easily solved and the solution is often employed to describe a variety of physical phenomena. In this work, a different model of radiation damping is considered for the spring-mass system. The (primary) spring is considered to possess mass. Air resistance is neglected, but an infinitely long (secondary or radiation) spring is considered to be attached to the mass. Thus, if the mass is set in motion, the infinite spring is excited and energy is carried out of the system. The mechanical wave in the secondary spring is analogous to radiation, and is referred to as mechanical radiation. Thus, while the mathematics of this system is more involved than that of the traditional damped oscillator, the model provides a more realistic description of radiation damping. The damping factor and frequencies are calculated for various choices of system parameters. The results of the calculation are generally consistent with expectation. Damping is clearly exhibited, and the frequencies are lowered by the damping. Damping is more important for the lower modes