Modelling Series RLC Circuit with Discrete Fractional Operator

Chatzarakis, George E.; Selvam, A. George Maria; Janagaraj, R.; Vignesh, D.

doi:10.1007/978-981-19-1111-8_79

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…Light damping is commonly seen in certain mechanical systems like the oscillation of a pendulum or a mass-spring system moving through a viscous medium. [10] cited that light damping can be found in electrical systems like RLC circuits where resistive losses cause damping to occur. If the students try moving the friction bar to the lots level, it will be observed that the oscillations decay as quickly as possible without oscillating.…”

Section: Dampingmentioning

confidence: 99%

Simple Harmonic Oscillation using Computer Simulation: Compilation of Experiments for Classroom Investigations

Pacala

2023

EJSMT

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The Simple Harmonic Oscillation (SHO) is a fundamental concept in physics, as it describes a large variety of phenomena that occur in nature, such as the motion of pendulums, mass-spring systems, and atoms. A thorough understanding of SHO can provide a good foundation for learning more advanced topics in physics, making it an essential topic for students to learn. Computer simulation technology provides an effective way to model SHO phenomena in the classroom. This technology allows students to explore SHO concepts visually and to replicate experiments that would be cumbersome or impossible to conduct otherwise. However, there are few compilations of SHO simulations appropriate for classroom use. This paper presented a compilation of SHO experiments that utilize computer simulation of PhET. The compiled experiments cover a broad range of SHO concepts, including proving the relationship of energy and amplitude, velocity and displacement, acceleration and displacement and types of damping. These experiments are suitable for classrooms of all levels and can be used to broaden and enrich students' understanding of SHO. Overall, the simulation-based experiments presented here offer a valuable resource for educators seeking to improve their students' understanding of SHO.

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Section: Dampingmentioning

confidence: 99%

Simple Harmonic Oscillation using Computer Simulation: Compilation of Experiments for Classroom Investigations

Pacala

2023

EJSMT

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Application of fractional modified taylor wavelets in the dynamical analysis of fractional electrical circuits under generalized caputo fractional derivative

Rayal,

Anand,

Srivastava

2024

Phys. Scr.

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This study examines the application of fractional calculus in the analysis and modeling of electrical circuits of fractional order, highlighting its potential to explain the behaviour of complex electrical circuits accurately. In the domain of electrical circuits, fractional differential equations are employed in the analysis and simulation of systems that consist of resistors, capacitors and inductors. In the present paper, a novel approach utilizing fractional order modified Taylor wavelets is implemented to solve the fractional model of RL, LC, RC and RLC electrical circuits under generalized Caputo fractional derivative which offers precise and flexible modeling of non-locality and hereditary characteristics in complex systems. Furthermore, an additional parameter $\sigma$ (time scale parameter) is incorporated in fractional circuit dynamics to maintain the physical dimensionality. The considered wavelets with the collocation technique offer an efficient solution by converting the fractional model of electrical circuits into a set of algebraic equations which are further solved by using the Newton iteration method. Moreover, this study discusses the significance of Ulam-Hyers stability, emphasizing its role in ensuring stable and reliable circuit performance. The impact of fractional order on the dynamics of the electric circuit model is presented by tables and graphs. The approximate solutions obtained by the proposed method are well comparable with exact solutions and some other existing wavelet-based techniques. The residual errors are also evaluated under various model parameters for fractional orders. Furthermore, the graphs illustrate that the error progressively decreases as the number of wavelets basis increases.

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Chaotic dynamics of fractional difference magnetic levitation model with application to image encryption

Vignesh

Fataf

2023

Eur. Phys. J. Spec. Top.

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Modelling Series RLC Circuit with Discrete Fractional Operator

Cited by 3 publications

References 19 publications

Simple Harmonic Oscillation using Computer Simulation: Compilation of Experiments for Classroom Investigations

Simple Harmonic Oscillation using Computer Simulation: Compilation of Experiments for Classroom Investigations

Application of fractional modified taylor wavelets in the dynamical analysis of fractional electrical circuits under generalized caputo fractional derivative

Chaotic dynamics of fractional difference magnetic levitation model with application to image encryption

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