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A single program deck, with individual subroutines marked. The markings show the effects of editing, as cards are replaced or reordered. Many early programming languages, including FORTRAN, COBOL and the various IBM assembler languages, used only the first 72 columns of a card – a tradition that traces back to the IBM 711 card reader used on the IBM 704/709/7090/7094 series (especially the ...
A periodic motion is a closed curve in phase space. That is, for some period, ′ = (,), = (). The textbook example of a periodic motion is the undamped pendulum.. If the phase space is periodic in one or more coordinates, say () = (+), with a vector [clarification needed], then there is a second kind of periodic motions defined by
An IBM 80-column punched card of the type most widely used in the 20th century IBM 1442 card reader/punch for 80 column cards. A computer punched card reader or just computer card reader is a computer input device used to read computer programs in either source or executable form and data from punched cards.
The periodic solution is one of the (,) and (,), called a Mathieu function of the first kind of integral order. The nonperiodic one is denoted either fe n ( x , q ) {\displaystyle {\text{fe}}_{n}(x,q)} and ge n ( x , q ) {\displaystyle {\text{ge}}_{n}(x,q)} , respectively, and is called a Mathieu function of the second kind (of integral order).
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of f ( t ) {\displaystyle f(t)} , solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. [ 3 ]
In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail.
As an aid to humans who had to deal with the punched cards, the IBM 026 and later 029 and 129 key punch machines could print human-readable text above each of the 80 columns. Invalid "lace cards" such as this pose mechanical problems for card readers. As a prank, punched cards could be made where every possible punch position had a hole.
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