An analytically solvable model of dissipation

The initial energy of a pendulum weakly coupled to a stretched string of infinite length dissipates into waves traveling away along the string. The frequency spectrum of this process emerges from a simple algebraic procedure resting on its key features. Confining the string to a long but finite length revives the pendular motion periodically. This model illustrates basic aspects of dissipation, providing material for exercises on physicomathematical techniques.