8 papers · 1 filter
An alternative approach to several important systems in classical mechanics: energy factorization
Karlo Lelas, Dario JukiÄ
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using com…
Damped harmonic oscillator revisited: a new approach to energy decay in the case of Coulomb, Stokes, and Newton damping
Robert Pezer, Karlo Lelas
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proport…
New approach to approximate analytical solutions of a harmonic oscillator with weak to moderate nonlinear damping: Part I
Karlo Lelas, Robert Pezer
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces…
Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)
Karlo Lelas, Robert Pezer
We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding f…
The amplitude decay of a harmonic oscillator damped simultaneously by weak linear and nonlinear damping forces
Karlo Lelas, Robert Pezer
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant mag…
Optimal damping adapted to a set of initial conditions
Karlo Lelas
Vibrating systems can respond to an infinite number of initial conditions and the overall dynamics of the system can be strongly affected by them. Therefore, it is of practical imp…