18 citations · 77 across the 17 of their papers we have counts for
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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…
An alternative approach to several important systems in classical mechanics: energy factorization
Karlo Lelas, Dario Jukić
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…
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…
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…
Driven damped harmonic oscillator revisited: energy resonance
Karlo Lelas, Nikola Poljak
We derive the exact expression for the resonant frequency of the time-averaged steady-state energy and show that this frequency is excellently approximated by the arithmetic mean o…
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…
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…
Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick
Karlo Lelas, Robert Pezer
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the ass…
Optimal damping of vibrating systems: dependence on initial conditions
K. Lelas, I. Nakić
Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed th…
Damped harmonic oscillator revisited: the fastest route to equilibrium
Karlo Lelas, Nikola Poljak, Dario Jukić
Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically da…