Campos, Luis Manuel Braga da Costa creator author. text bibliography flu 2018 monographic eng 1 online resource (pages cm.) Linear Differential Equations and Oscillators is the first book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This first book consists of chapters 1 and 2 of the fourth volume. The first chapter covers linear differential equations of any order whose unforced solution can be obtained from the roots of a characteristic polynomial, namely those: (i) with constant coefficients; (ii) with homogeneous power coefficients with the exponent equal to the order of derivation. The method of characteristic polynomials is also applied to (iii) linear finite difference equations of any order with constant coefficients. The unforced and forced solutions of (i,ii,iii) are examples of some general properties of ordinary differential equations. The second chapter applies the theory of the first chapter to linear second-order oscillators with one degree-of-freedom, such as the mechanical mass-damper-spring-force system and the electrical self-resistor-capacitor-battery circuit. In both cases are treated free undamped, damped, and amplified oscillations; also forced oscillations including beats, resonance, discrete and continuous spectra, and impulsive inputs. Describes general properties of differential and finite difference equations, with focus on linear equations and constant and some power coefficients Presents particular and general solutions for all cases of differential and finite difference equations Provides complete solutions for many cases of forcing including resonant cases Discusses applications to linear second-order mechanical and electrical oscillators with damping Provides solutions with forcing including resonance using the characteristic polynomial, Green' s functions, trigonometrical series, Fourier integrals and Laplace transforms Luis Manuel Braga da Campos. Vibrators Mathematical models Mechanical movements Mathematical models Oscillations Mathematical models Differential equations, Linear MATHEMATICS / Applied MATHEMATICS / Differential Equations MEDICAL / General TJ208 .C36 2018 621.8 9780429028984 (electronic bk) 0429028989 (electronic bk) 9780429642791 0429642792 9780429639623 0429639627 9780429636455 0429636458 https://www.taylorfrancis.com/books/9780429028984 http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf https://www.taylorfrancis.com/books/9780429028984 http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf OCoLC-P 191107 20260210180819.0 9780429028984 eng