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