Finding Solutions to Undamped and Damped Simple Harmonic Oscillations via Kashuri Fundo Transform
Abstract
Differential equations are expressions that are frequently encountered in mathematical modeling of laws or problems in many different fields of science. It can find its place in many fields such as applied mathematics, physics, chemistry, finance, economics, engineering, etc. They make them more understandable and easier to interpret, by modeling laws or problems mathematically. Therefore, solutions of differential equations are very important. Many methods have been developed that can be used to reach solutions of differential equations. One of these methods is integral transforms. Studies have shown that the use of integral transforms in the solutions of differential equations is a very effective method to reach solutions. In this study, we are looking for a solution to damped and undamped simple harmonic oscillations modeled by linear ordinary differential equations by using Kashuri Fundo transform, which is one of the integral transforms. From the solutions, it can be concluded that the Kashuri Fundo transform is an effective method for reaching the solutions of ordinary differential equations.
Keywords
Kashuri Fundo transform, inverse Kashuri Fundo transform, undamped simple harmonic oscillation, damped simple harmonic oscillation, differential equation
References
- Zill D.G., A First Course in Differential Equations with Modeling Applications, 11th ed. Cengage Learning, 2017.
- Hairer E., Norsett S.P. and Wanner G., Solving Ordinary Differential Equations I: Nonstiff Problems, Berlin, New York: Springer-Verlag, 1993.
- Hand L.N. and Finch J.D., Analytical Mechanics, Cambridge, UK: Cambridge University Press, 1998.
- Fowles G.R. and Cassiday G.L., Analytical Mechanics, 7th ed. Brooks/Cole, 2004.
- Fasano A. and Marmi S., Analytical Mechanics, USA: Oxford University Press, 2006.
- Debnath L. and Bhatta D., Integral Transforms and Their Applications, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC, 2007.
- Bracewell R.N., The Fourier Transform and Its Applications, 3rd ed. New York, USA: McGraw-Hill, 1986.
- Widder D.V., The Laplace Transform. Princeton, USA: Princeton University Press, 1946.
- Watugala G.K., ”Sumudu Transform: A New Integral Transform to Solve Differential Equations and Control Engineering Problems”, International Journal of Mathematical Education in Science and Technology, 24, (1993), 35-43.
- Al-Omari S.K.Q., ”On the Application of Natural Transforms”, International Journal of Pure and Applied Mathematics, 85(4), (2013), 729-744.