On Oscillations I

"Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens; and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter experience - changes which require millions of years for their accomplishment." (Mary Somerville, "The Connection of the Physical Sciences", 1834)

"Ask your imagination if it will accept a vibrating multiple proportion - a numerical ratio in a state of oscillation? I do not think it will. You cannot crown the edifice with this abstraction. The scientific imagination, which is here authoritative, demands, as the origin and cause of a series of ether-waves, a particle of vibrating matter quite as definite, though it may be excessively minute, as that which gives origin to a musical sound. Such a particle we name an atom or a molecule. I think the intellect, when focused so as to give definition without penumbral haze, is sure to realize this image at the last." (John Tyndall, "Fragments of Science for Unscientific People", 1871)

"Certain exterior impulses hit the economic mechanism and thereby initiate more or less regular oscillations." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"In reality the cycles we have the occasion to observe are generally not damped. How can the maintenance of the swings be explained? Have theses dynamic laws deduced from theory and showing damped oscillations no value in explaining the real phenomena, or in what respect do the dynamic laws need to be completed in order to explain the real happenings? They (dynamic laws) only form one element of the explanation: they solve the propagation problem. But the impulse problem remains." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"The majority of the economic oscillations which we encounter seem to be explained most plausibly as free oscillations." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"In the field of oscillations, there takes place a sharply distinct interaction between physics and mathematics, as well as influence of physics’ needs on the development of mathematical methods and mathematics’ feedback towards our physical knowledge." (Alexander A Andronov et al, "Theory of Oscillators", 1966)

"However, and conversely, our models fall far short of representing the world fully. That is why we make mistakes and why we are regularly surprised. In our heads, we can keep track of only a few variables at one time. We often draw illogical conclusions from accurate assumptions, or logical conclusions from inaccurate assumptions. Most of us, for instance, are surprised by the amount of growth an exponential process can generate. Few of us can intuit how to damp oscillations in a complex system." (Donella H Meadows, "Limits to Growth", 1972)

"[…] the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks." (George Pólya, "Mathematical Methods in Science", 1977)

"There is probably no exaggeration to say that among the processes as freely occurring in nature as used in engineering, oscillations to be understood in the broadest sense of the word, in many respects occupy a prominent and often dominant place. [...] The development of the study of oscillations is inextricably tied up with the development of mathematical methods for their treatment." (Nikolai D Papaleksy)