Simple harmonic motion (SHM) is studied and shown to be intimately related to uniform circular motion. Oscillations of a mass-spring system, as well as of a pendulum, are studied. The differential equation of SHM is derived.

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Introduction to Mechanics of Particles and Systems

Introduction to Mechanics of Particles and Systems

Costas J. Papachristou

Introduction to Mechanics of Particles and Systems


Costas J. Papachristou Department of Physical Sciences Hellenic Naval Academy Piraeus, Greece

ISBN 978-3-030-54270-2 ISBN 978-3-030-54271-9 https://doi.org/10.1007/978-3-030-54271-9


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Newtonian Mechanics is, traditionally, the first stage of “initiation” of a college student into Physics. It is perhaps the only truly autonomous subject area of Physics, in the sense that it can be taught as a self-contained entity without the need for support from other areas of physical science. This textbook is based on lecture notes (originally in Greek) used by this author in his two-semester course of introductory Mechanics, taught at the Hellenic Naval Academy (the Naval Academy of Greece). It is evident that no serious approach to Mechanics (at least at the university level) is possible without the support of higher Mathematics. Indeed, the central law of Mechanics, Newton’s Second Law, carries a rich mathematical structure being both a vector equation and a differential equation. An effort is thus made to familiarize the student from the outset with the use of some basic mathematical tools, such as vectors, differential operators, and differential equations. To this end, the first chapter contains the elements of vector analysis that will be needed in the sequel, while the Mathematical Supplement constitutes a brief introd