Volume-12 , Issue-5 , Oct 2024, ISSN 2348-3423 (Online) Go Back

• Open Access   Article

  Bianchi Type-VIO String Cosmological Model in f(R,T) Theory of Gravity

  S.P. Gaikwad, A.K. Dabre, K.R. Mule

  Research Paper | Journal-Paper (IJSRPAS)

  Vol.12 , Issue.5 , pp.1-6, Oct-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  This paper investigates a spatially homogeneous and anisotropic Bianchi type-VIo universe with a string of clouds in the framework of gravitational theory. The field equations were found by considering the proportionality of the expansion scalar ? and the shear scalar ?. Some cosmologically crucial physical and kinematical characteristics of the model are determined, and their geometric relevance is addressed.

  Key-Words / Index Term
  Bianchi type-VIo, Cosmic string, gravity

  References
  [1] S. Perlmutter et al., ‘Measurements* of the Cosmological Parameters ? and ? from the First Seven Supernovae at z? 0.35’, The astrophysical journal, Vol.483, No.2, pp.565, 1997.
  [2] S. Perlmutter et al., ‘Discovery of a supernova explosion at half the age of the Universe’, Nature, Vol.391, No.6662, pp.51–54, 1998. https://doi.org/10.1038/34124
  [3] A. G. Riess et al., ‘Observational evidence from supernovae for an accelerating universe and a cosmological constant’, The astronomical journal, Vol.116, No.3, pp.1009, 1998.
  [4] C. L. Bennett et al., ‘The microwave anisotropy probe* mission’, The Astrophysical Journal, Vol.583, No.1, pp.1, 2003.
  [5] T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, ‘f (R, T) gravity’, Physical Review D—Particles, Fields, Gravitation, and Cosmology, Vol.84, No.2, p.024020, 2011. https://doi.org/10.1103/PhysRevD.84.024020
  [6] M. V. Dawande, K. S. Adhav, and S. S. Nerkar, ‘LRS Bianchi Type-I Universe in F (T) Theory of Gravity’, Advances in Astrophysics, Vol.2, No.2, pp.117–125, 2017.
  [7] M. Sharif, M. Zubair, J. Phys. Soc. Jpn. 81, 114005, 2012.
  [8] K. L. Mahanta, ‘Bulk viscous cosmological models in f(R, T) theory of gravity’, Astrophysics and Space Science, vol.353, pp.683–689, 2014. https://doi.org/10.1007/s10509-014-2040-6
  [9] R. L. Naidu, D. R. K. Reddy, T. Ramprasad, and K. V. Ramana, ‘Bianchi type-V bulk viscous string cosmological model in f (R, T) gravity’, Astrophysics and Space Science, Vol.348, pp.247–252, 2013. https://doi.org/10.1007/s10509-013-1540-0
  [10] N. Ahmed and A. Pradhan, ‘Bianchi type-V cosmology in f (R, T) gravity with ? (T)’, International Journal of Theoretical Physics, Vol.53, No.1, pp.289–306, 2014. https://doi.org/10.1007/s10773-013-1809-7
  [11] K. Pawar and A. Dabre, ‘Perfect Fluid Coupled String Universe in f (R, T) Gravity’, Journal of Scientific Research, Vol.15, No.3, pp.695–704, 2023. http://doi.org/10.3329/jsr.v15i3.64173
  [12] A. Y. Shaikh and S. R. Bhoyar, ‘Plane Symmetric Universe with ? in f (R, T) Gravity’, Prespacetime Journal, Vol.6, No.11, 2015.
  [13] J. D. Barrow, ‘Helium formation in cosmologies with anisotropic curvature’, Monthly Notices of the Royal Astronomical Society, Vol.211, No.2, pp.221–227, 1984. https://doi.org/10.1093/mnras/211.2.221
  [14] K. D. Krori, T. M. Chaudhuri, and C. R. Mahanta, ‘C R. and Mazumdar’, A. Gen. Relativ. Gravit, Vol.22, No.990, pp.123, 1990.
  [15] R. Tikekar and L. K. Patel, ‘Some exact solutions in Bianchi VI0 string cosmology’, Pramana, Vol.42, pp.483–489, 1994. https://doi.org/10.1007/BF02847130
  [16] R. Bali, R. Banerjee, and S. K. Banerjee, ‘Some LRS Bianchi Type VI0 Cosmological Models with Special Free Gravitational Fields’, Electronic J. of Theoretical Phy., Vol.6, No.21, 2009.
  [17] P. Mahanta and A. Mukherjee, ‘String models in Lyra geometry’, Indian Journal of Pure and Applied Mathematics, Vol.32, No.2, pp.199–204, 2001.
  [18] R. Bhattacharjee and K. K. Baruah, ‘String cosmologies with a scalar field’, Indian J. Pure Appl. Math. vol. 32, pp 7–53, 2001.
  [19] P. S. Letelier, ‘String cosmologies’, Physical review D, vol. 28, no. 10, p. 2414, 1983.
  [20] D. C. Maurya, A. Dixit, and A. Pradhan, ‘Transit string dark energy models in f (Q) gravity’, International Journal of Geometric Methods in Modern Physics, vol. 20, no. 08, p. 2350134, 2023. https://doi.org/10.1142/S0219887823501347
  [21] R. Zia, D. C. Maurya, and A. Pradhan, ‘Transit dark energy string cosmological models with perfect fluid in F (R, T)-gravity’, International Journal of Geometric Methods in Modern Physics, vol. 15, no. 10, p. 1850168, 2018. https://doi.org/10.1142/S0219887818501682
  [22] S. Rani, J. K. Singh, and N. K. Sharma, ‘Bianchi type-III magnetized string cosmological models for perfect fluid distribution in f (R, T) gravity’, International Journal of Theoretical Physics, Vol.54, pp.1698–1710, 2015. https://doi.org/10.1007/s10773-014-2371-7
  [23] S. Ram and S. Chandel, ‘Dynamics of magnetized string cosmological model in f (R, T) gravity theory’, Astrophysics and Space Science, Vol.355, pp.195–202, 2015. https://doi.org/10.1007/s10509-014-2160-z
  [24] R. Bali, U. K. Pareek, and A. Pradhan, ‘Bianchi type-I massive string magnetized barotropic perfect fluid cosmological model in general relativity’, Chinese Physics Letters, vol. 24, no. 8, p. 2455, 2007.
  [25] K. Pawar, A. K. Dabre, and N. T. Katre, ‘Anisotropic String Cosmological Model for Perfect Fluid Distribution in f (T) Gravity’, Int. J. Sci. Res. in Physics and Applied Sciences Vol, vol. 10, no. 6, 2022. https://doi.org/10.26438/ijsrpas/v10i6.17
  [26] A. Pradhan, H. Amirhashchi, and H. Zainuddin, ‘Exact solution of perfect fluid massive string cosmology in Bianchi type III space-time with decaying vacuum energy density ?’, Astrophysics and Space Science, vol. 331, no. 2, pp. 679–687, 2011. https://doi.org/10.1007/s10509-010-0469-9
  [27] A. Tyagi, S. Parikh, and Tripathi B. R. ‘Inhomogeneous Bianchi Type-I Cosmological Model For Stiff Perfect Fluid Distribution’, Prespacetime Journal, vol 7(12), 2016.
  [28] K. Pawar, A. K. Dabre, ‘Bulk Viscous String Cosmological Model with Power Law Volumetric Expansion in Teleparallel Gravity’, Astrophysics, Vol.66, Issue.1, pp.114-126, 2023.
  [29] K. Pawar, A. K. Dabre, and P. Makode. ‘Plane Symmetric String Cosmological Model with Zero Mass Scalar Field in f(R) Gravity’, Astrophysics, Vol.66, No.3, pp.353-365, 2023.
  [30] K. Pawar and A. K. Dabre, ‘Bulk Viscous String Cosmological Model with Constant Deceleration Parameter in Teleparallel Gravity’, Int. J. Sci. Res. in Physics and Applied Sciences, Vol.10, No.6, 2022. DOI: https://doi.org/10.26438/ijsrpas/v10i6.816

  Citation
  S.P. Gaikwad, A.K. Dabre, K.R. Mule, "Bianchi Type-VIO String Cosmological Model in f(R,T) Theory of Gravity," International Journal of Scientific Research in Physics and Applied Sciences, Vol.12, Issue.5, pp.1-6, 2024

• Open Access   Article

  Introducing a Method to Determine the Radius of a Water Drop of Tap

  Toyesh Prakash Sharma, Etisha Sharma

  Research Paper | Journal-Paper (IJSRPAS)

  Vol.12 , Issue.5 , pp.7-14, Oct-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Under the title; introducing a method to determine the radius of a water drop of tap, we are trying to calculate the radius of the water drop of a normal tap under some specific conditions which we are talking about in introduction section of the paper. Everyone can easily perform this experiment since it contains the basic mathematical concepts and use of conservation of volume. This experiment has two parts one is dealing with the object to determine the radius of the water drop falling from a synchronized tap while the other part is dealing the object to compare the radii of drop and tap. For first part we have required a beaker, meter scale and watch while the other part require vernier caliper and a tap.

  Key-Words / Index Term
  Vernier calipers, Main Scale, Water drop, Volume, Radius, Surface tension, Stokes Law etc

  References
  [1] B. Zhang, V. Sanjay, S. Shi, Y. Zhao, C. Lv, and X.-Q. Feng, “Impact forces of water drops falling on superhydrophobic surfaces,” Phys. Rev. Lett., Vol.129, No.10, pp.104501-104510, 2022.
  [2] R. A. Ogden, K. F. Falk, M. D. Johnson, “Drop-weight method for determining water drop size,” Phys. Fluids, Vol.17, No.6, pp.62107-62115, 2005.
  [3] A. L. Yarin, "Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing," Annual Review of Fluid Mechanics, Vol.38, pp.159-183, 2006.
  [4] M. Rein and S. Thoroddsen, "Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading," Journal of Fluid Mechanics, Vol.852, pp.114–148, 2018.
  [5] L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. Oxford, UK: Pergamon Press, pp.2-5, 1987.

  Citation
  Toyesh Prakash Sharma, Etisha Sharma, "Introducing a Method to Determine the Radius of a Water Drop of Tap," International Journal of Scientific Research in Physics and Applied Sciences, Vol.12, Issue.5, pp.7-14, 2024

• Open Access   Article

  Simulation and Optical Absorption Analysis of Cr3+ doped Single Crystals of Potassium Magnesium Sulfate Chloride (Kainite)

  Maroj Bharati, Vikram Singh, Ram Kripal

  Research Paper | Journal-Paper (IJSRPAS)

  Vol.12 , Issue.5 , pp.15-20, Oct-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The zero field and crystal field splitting parameters for single crystals of Potassium Magnesium Sulphate Chloride (Kainite), KMgCST (KMgClSO4.3H2O) doped with Cr3+ ions are ascertained utilizing superposition model. For computation, the proper positions of the Cr3+ ions in the distorted KMgCST are considered. The zero field splitting parameters that are computed using local distortion closely match the values observed in experiments. The optical energy values for Cr3+ in KMgCST are estimated using the Crystal Field Analysis Program and crystal field parameters. The results show that a Cr3+ ion replaces one Mg2+ ion in KMgCST single crystals.

  Key-Words / Index Term
  Cr3+ ions in KMgCST; Crystal field; Optical spectroscopy; Superposition model; Zero-field splitting; EPR

  References
  [1] Dinabandhu Halder, Yatrta mohan Jana, Danuta Piwowarska, Pawel Gnutek, Czeslaw Rudowicz, “Tailoring single-ion magnet properties of coordination polymer C11H18DyN3O9 (Dy-CP) using the radial effective charge model (RECM) and superposition model (SPM)”, Physical Chemistry Chemical Physics., Vol.26, pp.19947-19959, 2024.
  [2] Maroj Bharati, Vikram Singh, Ram Kripal, “Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals”, IgMin Research, Vol.2, Issue6, pp.484-489, 2024.
  [3] Shish Pal Rathee, S. S. Hooda, “EPR and superposition-model analysis of zero-field splitting parameters for Mn2+ doped in ZnNbOF5.6(H2O) and CoNbOF5.6(H2O) single crystals”, Indian Journal of Physics, 2024, https://doi.org/10.1007/s12648-024-03268-3
  [4] Maroj Bharati, Vikram Singh, Ram Kripal, “Zero Field Splitting Parameter of Mn2+ in PMN Single Crystals”, International Journal of Engineering Technology Research and Management, Vol.7, pp.43-52, 2023.
  [5] Muhammed Acikgoz, Ram Kripal, Madan Gopal Misra, Awadhesh Kumar Yadav, Pawel Gnutek, Czeslaw Rudowicz, “Theoretical analysis of crystal field parameters and zero field splitting parameters for Mn2+ ions in tetramethylammonium tetrachlorozincate”, Polyhedron, Vol. 235, p.116341, 2023.
  [6] Roman Boca, Cyril Rajnak, Jan Titis, “Zero-Field Splitting in Hexacoordinate Co(II) Complexes”, Magnetochemistry, Vol.9, pp. 100, 2023.
  [7] Maroj Bharati, Vikram Singh, Ram Kripal, “Modeling of Mn2+ doped CdGa2Se4 single crystals”, International Journal of Engineering Inventions, Vol.12, pp.170-175, 2023.
  [8] Ram Kripal, “Zero Field Splitting Parameter of Mn2+-Doped Tl2Cd2(SO4)3 Single Crystals at Axial Symmetry Site”, Acta Physica Polonica A, Vol.143, pp.217-220, 2023.
  [9] Sangita Pandey, Ram Kripal, Awadhesh Kumar Yadav, Muhmmed Aç?kg¨oz, Pawel Gnutek, Czeslaw Rudowicz,“Implications of direct conversions of crystal field parameters into zero-field splitting ones - Case study: Superposition model analysis for Cr3+ ions at orthorhombic sites in LiKSO4”, Journal of Luminiscence, Vol. 230, p. 117548, 2021.
  [10] Mitsuo Yamaga, Akhilesh Kumar Singh, Douglas Cameron, Pajul R. Edwards, Michal Bo?kowski, “Crystal-field analysis of photoluminescence from orthorhombic Eu centers and energy transfer from host to Eu in GaN co-doped with Mg and Eu”, Journal of Luminiscence., Vol. 270, Issue 6, p.120557, 2024.
  [11] B. Deva Prasad Raju, J. Lakshmana Rao, K.V. Narasimhulu, N. O. Gopal, C.S. Sunandana, “EPR and optical absorption studies on Cr3+ ions doped in KZnClSO4·3H2O single crystals”, Spectrochimica Acta Part A, Vol 61, pp.2195–2198, 2005.
  [12] M. A. Martin-Luengo, M.Yates, “Zeolitic materials as catalysts for organic syntheses”, Journalof Materials Sciience, Vol. 30, pp.4483-4491, 1995.
  [13] S. N. Reddy, R. V. S. S. N. Ravikumar, B. J. Reddy, Y. P. Reddy, P. S. Rao, “Spectroscopic investigations on Fe3+, Fe2+ and Mn2+ bearing antigorite mineral”, Neues Jahrbuch Fur Mineralogie-Monatshefte, Vol. 6, p.261, 2001.
  [14] S. Dhanuskodi, A. Pricilla Jeyakumari, “EPR studies of Cr3+ ions in kainite single crystals”, Matials Chemistry and Physics, Vol. 87, pp.292–296, 2004.
  [15] Paul D. Robinson, J. H. Fang, Y. Ohya, “The Crystal Structure of Kainite”, The American Mineralogist, Vol. 57, pp.1325-1332, 1972.
  [16] Czeslaw Rudowicz, Miroslaw Karbowiak, “Disentangling Intricate Web of Interrelated Notions at the Interface Between the Physical (Crystal Field) Hamiltonians and the Effective (Spin) Hamiltonians”, Coordination Chemistry Review, Vol.287, pp.28-63, 2015.
  [17] Czeslaw Rudowicz, “Concept of spin Hamiltonian, forms of zero field splitting and electronic Zeeman Hamiltonians and relations between parameters used in EPR. A critical review”, Magnetic Resonance Review, Vol. 13, pp. 1-89, 1987, Erratum: Czdeslaw Rudowicz, Magnetic Resonance Review, Vol. 13, p. 335, 1988.
  [18] S. I. Nikitin, E. M. Kutashova, R.V.Yusupov, R. I. Karimov, A. G. Kiiamov, “Laser spectroscopy and crystal field analysis of energy level structure of Tm3+ ions in SrY2O4 crystal” Journal of Luminiscence., Vol. 272, Issue 8, p.120616, 2024.
  [19] Czeslaw Rudowicz, “Transformation Relations for theConventional Okq and NormalisedO’kq Stevens Operator equivalents with k=1 to 6 and -k ?q? k”, Journal of Physics C: Solid State Physics, Vol. 18, pp.1415-1430, 1985, Erratum: Czeslaw Rudowicz, Journal of Physics C: Solid State Physics, Vol. 18, p.3837, 1985.
  [20] Czeslaw Rudowicz, C. Y. Chung, „The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements”, Journal of Physics: Condensed Matter, Vol.16, pp.5825-5847, 2004.
  [21] D. J. Newman, B. Ng, “Superposition model”, Ch. 5 in:Newman D J, Ng B. (Eds.). “Crystal Field Handbook”, Cambridge University Press, UK, pp. 83–119, 2000.
  [22] D. J. Newman, B. Ng, “The Superposition model of crystal fields“, Reports of Progress in Physics, Vol. 52, pp. 699-763, 1989.
  [23] Czeslaw Rudowicz, “On the Derivation of the Superposition-Model Formulae Using the Transformation Relations for the Stevens Operators”, Journal of Physics C: Solid State Physics, Vol.20, pp.6033-6037, 1987.
  [24] Czeslaw Rudowicz, Pawel Gnutek, Muhmmed Acikgoz,“Superposition Model in Electron Magnetic Resonance Spectroscopy-A Primer for Experimentalists with Illustrative Applications and Literature Database”, Applied Spectroscopy Review, Vol.54, pp.673-718, 2019.
  [25] Muhmmred Aç?kgöz, „A study of the impurity structure for 3d3 (Cr3+ and Mn4+) ions doped into rutile TiO2 crystal“, Spectrochimica Acta A, Vol. 86, pp.417-422, 2012.
  [26] K.A. Müller, W. Berlinger, J. Albers, „Paramagnetic resonance and local position of Cr3+ in ferroelectric BaTiO3“, Physical Review B, Vol. 32, pp. 5837-5850, 1985.
  [27] K. A. Muller, W. Berlinger, “Superposition Model for Sixfold-Coordinated Cr3+ in Oxide Crystals (EPR Study)”, Journal of Physics C: Solid State Physics, Vol. 16, pp.6861-6874, 1983.
  [28] T. H. Yeom, Y. M. Chang, Czeslaw Rudowicz, S. H.Choh, “Cr3+ Centres in LiNbO3: Experimental and Theoretical Investigation of Spin Hamiltonian Parameters”, Solid State Communications, Vol. 87, pp.245-249, 1993.
  [29] E. Siegel, K. A. Muller, “Structure of Transition-Metal-Oxygen-Vacancy Pair Centers”,Physical Review B, Vol. 19, pp.109-120, 1979.
  [30] Czeslaw Rudowicz, Richard Bramley, „On standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry”, Journal of Chemical Physics, Vol. 83, pp. 5192-5197, 1985.
  [31] Y.Y. Yeung, D. J. Newman, “Superposition-model analyses for the Cr3+ 4A2 ground state”, Physical. Review B, Vol.34, pp.2258-2265, 1986.
  [32] Y. Y. Yeung, Czeslaw Rudowicz, “Ligand Field Analysis of the 3dN Ions at Orthorhombic or Higher Symmetry Sites”, Computers and Chemistry, Vol.16, pp.207-216, 1992.
  [33] Y. Y. Yeung, Czeslaw Rudowicz, “Crystal Field Energy Levels and State Vectors for the 3dN Ions at Orthorhombic or Higher Symmetry Sites”, Journal of Computational Physics, Vol.109, pp.150-152, 1993.
  [34] Y. M. Chang, Czeslaw Rudowicz, Y.Y.Yeung, “Crystal field analysis of the 3dN ions at low symmetry sites including the ‘imaginary’ terms”, Computers in Physics, Vol. 8, pp.583-588, 1994.
  [35] B. G. Wybourne, “Spectroscopic Properties of Rare Earth”, Wiley, New York, USA, 1965.
  [36] B. N. Figgis, M.A. Hitchman, “Ligand Field Theory and its Applications”, Wiley, New York, USA, 2000.
  [37] Sadao Adachi, “Photoluminescence Spectroscopy and Crystal-Field Parameters of Cr3+ Ion in Red and Deep Red-Emitting Phosphors“, ECS Journal of Solid State Science and Technology, Vol.8, pp.R164-R168, 2019.
  [38] Sadao Adachi, “Review—Photoluminescence Properties of Cr3+-Activated Oxide Phosphors“, ECS Journal of Solid State Science and Technology, Vol. 10, p. 026001, 2021.

  Citation
  Maroj Bharati, Vikram Singh, Ram Kripal, "Simulation and Optical Absorption Analysis of Cr3+ doped Single Crystals of Potassium Magnesium Sulfate Chloride (Kainite)," International Journal of Scientific Research in Physics and Applied Sciences, Vol.12, Issue.5, pp.15-20, 2024

• Open Access   Article

  Application of Laplace Transform in Physics for Solving Ordinary Differntial Equations

  Toyesh Prakash Sharma, Etisha Sharma

  Research Paper | Journal-Paper (IJSRPAS)

  Vol.12 , Issue.5 , pp.21-30, Oct-2024

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The Laplace transform is a crucial tool in solving complex physical problems in physics by converting differential equations into algebraic ones. This paper explores its applications in electromagnetism, classical mechanics, and thermodynamics. It demonstrates how the Laplace transform simplifies the analysis of electrical circuits, wave propagation, and heat conduction. The research highlights its effectiveness through examples, providing a framework for researchers to address complex challenges and advance understanding in various physical domains.

  Key-Words / Index Term
  Laplace transform, Lagrangian Mechanics, Integral transform, Simple pendulum, compound pendulum etc

  References
  [1] R. E. Bellman and R. E. Kalaba, Selected Papers on the Laplace Transform. New York, NY: Dover Publications, 1966.
  [2] P. P. Gupta, Laplace Transforms: A Comprehensive Introduction. New Delhi, India: McGraw-Hill Education, 2015.
  [3] H. Chen and Y. Zhang, "Laplace transform for stable random variables," in Proc. IEEE 3rd Int. Conf. Comput. Comput. Sci., 2015.
  [4] P. Szymczyk and M. Szymczyk, "Classification of geological structure using ground penetration radar and Laplace transform artificial neural networks," Neurocomputing, Vol.148, pp.354-362, 2015.
  [5] S. Gupta, D. Kumar, and J. Singh, "Analytical solutions of convection-diffusion problems by combining Laplace transform method and homotopy perturbation," Alexandria Eng. J., Vol.54, pp.645-651, 2015.
  [6] W. K. Zahra, M. M. Hikal, and A. T. Bahnasy, "Solutions for fractional order electrical circuits in Laplace transform and non-standard finite difference method," J. Egyptian Math. Soc., pp.1-10, 2017.
  [7] J. S. Lilley, Nuclear Physics: Principles and Applications. Chichester, UK: Wiley, pp.34-37, 2001.
  [8] J. C. Upadhyaya, Classical Mechanics, 2019 ed. New Delhi, India: Himalaya Publishing House, ch. Lagrangian Dynamics, pp.44-45, 2019.
  [9] J. C. Upadhyaya, Classical Mechanics, 3rd ed. Mumbai, India: Himalaya Publishing House, pp.47, 2019.
  [10] P. Beeken, "Atwood’s heavy chain," The Physics Teacher, vol. 49, pp.470-472, 2011.
  [11] T. B. Greenslade Jr., "Atwood’s machine," The Physics Teacher, Vol.29, pp.24-28, 1985.
  [12] T. S. Deis and W. R. Perkins, "Newton`s Law of Cooling and the Specific Heat of Liquids," IEEE Trans. Educ., Vol.13, No.3, pp.117-120, 1970, doi: 10.1109/TE.1970.4320397.
  [13] S. J. Chapman, Electric Machinery Fundamentals, 5th ed. New York, NY, USA: McGraw-Hill, pp.144-150, 2011.
  [14] M. T. Thompson, "Inductance calculation techniques — Part II: Approximations and handbook methods," IEEE Trans. Magnetics, vol. 30, no. 2, pp.118-125, 1994.
  [15] D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, 10th ed. Hoboken, NJ, USA: Wiley, pp.380-385, 2013.
  [16] R. H. Rand, "Damped oscillations in nonlinear systems," J. Sound and Vibration, Vol.22, No.3, pp.343-349, 1972.
  [17] H. Goldstein, C. Poole, and J. Safko, Classical Mechanics, 3rd ed. San Francisco, CA, USA: Addison-Wesley, pp.75-78, 2002
  

  Citation
  Toyesh Prakash Sharma, Etisha Sharma, "Application of Laplace Transform in Physics for Solving Ordinary Differntial Equations," International Journal of Scientific Research in Physics and Applied Sciences, Vol.12, Issue.5, pp.21-30, 2024