Applications of Novel Integral transform: 'Kuffi-Abbas-Jawad' (KAJ) Transform to Damped Mechanical and Electrical Oscillators
DOI:
https://doi.org/10.31642/JoKMC/2018/120210Keywords:
'Kuffi-Abbas-Jawad' (KAJ) transform, 'Kuffi-Abbas-Jawad' (KAJ) transform inverse, Damped Mechanical , Electrical Oscillators, Differential Equation Responses.Abstract
This study utilizes the 'Kuffi-Abbas-Jawad' (KAJ) transform to determine the responses of mechanical and electrical oscillators. The paper introduces the KAJ transform as a novel approach for analyzing simple harmonic oscillators, as well as damped mechanical and electrical oscillators. Similar to other integral transform techniques, the 'Kuffi-Abbas-Jawad' (KAJ) transform serves as a practical and effective mathematical tool for obtaining these responses.
Downloads
References
[1] Said-Houari, B. (2016). Differential Equations: Methods and Applications. Springer. DOI: https://doi.org/10.1007/978-3-319-25735-8
[2] William E. Boyce, Richard C. DiPrima, “Elementary Differential Equations and Boundary Value Problems”, 10th edition, Wiley: USA, 2012.
[3] Gupta, R., Gupta, R., & Verma, D. (2019). Application of convolution method to the impulsive response of a lightly damped harmonic oscillator. International Journal of Scientific Research in Physics and Applied Sciences, 7(3), 173-175. DOI: https://doi.org/10.26438/ijsrpas/v7i3.173175
[4] Maktoof, S. F., Kuffi, E., & Abbas, E. S. (2021). “Emad-Sara Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24(7), 1985-1994. DOI: https://doi.org/10.1080/09720502.2021.1963523
[5] Zhang, X., & Tian, Y. (2022). Sharp conditions for the existence of positive solutions for a second-order singular impulsive differential equation. Applicable Analysis, 101(1), 1-13. DOI: https://doi.org/10.1080/00036811.2017.1370542
[6] Elzaki, T. M. (2012). Solution of nonlinear differential equations using mixture of Elzaki transform and differential transform method. In International Mathematical Forum (Vol. 7, No. 13, pp. 631-638).
[7] C. Jesuraj and A. Rajkumar, A New modified Sumudu Transform Called Raj Transform to Solve Differential Equations and Problems in Engineering and Science, International Journal on Engineering and Technologies, Vol. (11), N0. (2), (2020).
[8]. Sawant, L. S. (2018). Applications of Laplace transform in engineering fields. International Research Journal of Engineering and Technology, 5(5), 3100-3105.
[9]. Gupta, R., Gupta, R., & Rajput, S. (2019). Convolution method for the complete response of a series ł-Ɍ network connected to an excitation source of sinusoidal potential. International Journal of Research in Electronics And Computer Engineering, 7(1), 658-661.
[10]. Gupta, R., Talwar, L., & Gupta, R. (2019). Analysis of network circuit with steady voltage source, and with steady current source via convolution method. International journal of scientific & technology research, 8(11), 803-807.
[11]. Chitode, J. S., & Jalnekar, R. M. (2007). Network Analysis and Synthesis. Publisher: Technical Publications.
[12]. Van Valkenburg ,M. E.(2015), Network Analysis, 3rd Edition, Publisher: Pearson Education, [13]. Murray R. Spiegel, Theory and Problems of Laplace Transforms, Schaum's outline series, McGraw– Hill.
[14]. Gupta, R., Singh, A., & Gupta, R. (2020). Response of network circuits connected to Exponential excitation sources. International Advanced Research Journal in Science, Engineering and Technology, 7(2), 14-17.
[15]. Gupta, R. (2020). Impulsive responses of damped mechanical and electrical oscillators. International Journal of Scientific and Technical Advancements, 6(3), 41-44.
[16]. Gupta, R., Gupta, R., & Rajput, S. (2018). Analysis of damped harmonic oscillator by matrix method. International Journal of Research and Analytical Reviews (IJRAR).
[17]. Gupta, R., Gupta, R., & Rajput, S. (2018). Response of a parallel Ɫ-Ϲ-ℛ network connected to an excitation source providing a constant current by matrix method. International Journal for Research in Engineering Application & Management (IJREAM), 4(7), 212-217.
[18]. Gupta, R., Talwar, L., & Verma, D. (2020). Exponential excitation response of electric network circuits via residue theorem approach. Int. J. Sci. Res. in Multidisciplinary Studies Vol, 6(3), 4.
[19]. Gupta, R. (2022). Analysis of LCR Network Circuits with Exponential Sources by New Integral Transform Gupta Transform. Engineering and Scientific International Journal (ESIJ), 9(2), 27-29. DOI: https://doi.org/10.30726/esij/v9.i2.2022.92002
[20]. Gupta, R. (2020). Application of novel integral transform: gupta transform to mechanical and electrical oscillators. ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences, 4(1), 04-07.
[21]. Gupta, R. (2021). Gupta transform approach to the series RL and RC networks with steady excitation sources. Engineering and Scientific International Journal (ESIJ), 8(2), 45-47. DOI: https://doi.org/10.30726/esij/v8.i2.2021.82011
[22]. Gupta, R., Talwar, L., & Gupta, R. (2019). Analysis of network circuit with steady voltage source, and with steady current source via convolution method. International journal of scientific & technology research, 8(11), 803-807.
[23]. Moazzam, A., Kashif, M., Amjed, U., & Khawar, M. I. (2021). Devolpment of a new transformation to solve a new type of ordinary linear differential equation. Bulletin of Mathematics and Statistics Research (Bomsr), 9(3), 56-60.
[24. Burqan,A.; Qazza,A.; Saadeh,R.(2021), A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform. Mathematics, 9(23),1–14. DOI: https://doi.org/10.3390/math9233039
[25]. Saadeh, R., Qazza, A., & Amawi, K. (2022). A new approach using integral transform to solve cancer models. Fractal and Fractional, 6(9), 490. DOI: https://doi.org/10.3390/fractalfract6090490
[26]. Saadeh,R.; Qazza,A.; Burqan,A.; Khalil,R.(2022) Applications on Double ARA– Sumudu Transform in Solving Fractional Partial Differential Equations. Symmetry,14(9),1–17. DOI: https://doi.org/10.1155/2022/6939045
[27]. Akgül, A., Gökkaya, Z., Abbas, M., & Abdullah, F. A. (2023). New Applications of Fractional Differential Equations by General Integral Transforms. DOI: https://doi.org/10.21203/rs.3.rs-2657260/v1
[28]. Akgül, A., Ülgül, E., Sakar, N., Bilgi, B., & Eker, A. (2023). New applications of the new general integral transform method with different fractional derivatives. Alexandria Engineering Journal, 80, 498-505. DOI: https://doi.org/10.1016/j.aej.2023.08.064
[29]. Moazzzam, A., Anjum, A., Saleem, N., & Kuffi, E. A. (2023). Study of telegraph equation via he- fractional laplace homotopy perturbation technique. Ibn Al-Haitham Journal for Pure and Applied Sciences, 36(3), 349-364. DOI: https://doi.org/10.30526/36.3.3239
[30]. Fundamentals of Physics by Dr. Robert Resnick and David Halliday, 6th edition, Publisher: Wiley India Pvt Ltd.
[31]. Mansour, E. A., Kuffi, E. A., & Mehdi, S. A. (2021). On the SEE transform and systems of ordinary differential equations. Periodicals of Engineering and Natural Sciences (PEN), 9(3), 277-281.. DOI: https://doi.org/10.21533/pen.v9.i3.845
[32]. Mansour, E. A., Kuffi, E. A., & Mehdi, S. A. (2021). The new integral transform “SEE transform” and its applications. Periodicals of Engineering and Natural sciences (PEN), 9(2), 1016-1029. DOI: https://doi.org/10.21533/pen.v9.i2.803
[33]. Abbas, E. S., Kuffi, E. A., & Jawad, A. A. (2022). New integral “Kuffi-Abbas-Jawad” KAJ transform and its application on ordinary differential equations. Journal of Interdisciplinary mathematics, 25(5), 1427-1433. DOI: https://doi.org/10.1080/09720502.2022.2046339
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2025 Dr.Prakash Chand Thakur

This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.









