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1-60

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- Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

author

- Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

author

- Department of Systems Engineering, University of Lagos, Akoka, Lagos, Nigeria

author

- Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

author

- Department of Civil and Environmental Engineering, University of Lagos, Akoka, Lagos, Nigeria

author

- Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

References

- [1] G.L. Baker, J.A. Blackburn, The Pendulum: A Case Study in Physics, Oxford University Press, Oxford, 2005.
- [2] F.M.S. Lima, Simple ‘log formulae’ for the pendulum motion valid for any amplitude, Eur. J. Phys. 29 (2008) 1091–1098.
- [3] M. Turkyilmazoglu, Improvements in the approximate formulae for the period of the simple pendulum, Eur. J. Phys. 31 (2010) 1007–1011.
- [4] A. Fidlin, Nonlinear Oscillations in Mechanical Engineering, SpringerVerlag, Berlin Heidelberg, 2006.
- [5] R.E. Mickens, Oscillations in planar Dynamics Systems, World Scientific, Singapore, 1996.
- [6] J.H. He, NonPerturbative Methods for Strongly Nonlinear Problems, Disseration. deVerlag in Internet GmbH, Berlin, 2006.
- [7] W.P. Ganley, Simple pendulum approximation, Am. J. Phys. 53 (1985) 73–76.
- [8] L.H. Cadwell, E.R. Boyco, Linearization of the simple pendulum, Am. J. Phys. 59 (1991) 979–981.
- [9] M.I. Molina, Simple linearizations of the simple pendulum for any amplitude, Phys. Teach. 35 (1997) 489–490.
- [10] A. Beléndez, M.L. Álvarez, E. Fernández, I. Pascual, Cubication of conservative nonlinear oscillators, Eur. J. Phys. 30 (2009) 973–981.
- [11] E. Gimeno, A. Beléndez, Rational-harmonic balancing approach to nonlinear phenomena governed by pendulum-like differential equations, Z. Naturforsch. 64a (2009) 1–8.
- [12] F.M.S. Lima, A trigonometric approximation for the tension in the string of a simple pendulum accurate for all amplitudes, Eur. J. Phys. 30 (2009)
- [13] P. Amore, A. Aranda, Improved Lindstedt–Poincaré method for the solution of nonlinear problems, J. Sound Vib. 283 (2005) 1115–1136.
- [14] M. Momeni, N. Jamshidi, A. Barari and D.D. Ganji, Application of He’s Energy Balance Method to Duffing Harmonic Oscillators, International Journal of Computer Mathematics 88(1) (2010) 135–144.
- [15] S.S. Ganji, D.D. Ganji, Z.Z. Ganji and S. Karimpour, Periodic Solution for Strongly Nonlinear Vibration Systems by He’s Energy Balance Method. Acta Appl Math (2009) 106: 79. https://doi.org/10.1007/s10440-008-9283-6
- [16] H. Askari, M. Kalami Yazdi and Z. Saadatnia, Frequency analysis of nonlinear oscillators with rational restoring force via He’s Energy Balance Method and He’s Variational Approach, Nonlinear Sci Lett A 1 (2010) 425–430.
- [17] H. Babazadeh, G. Domairry, A. Barari, R. Azami and A.G. Davodi, Numerical analysis of strongly nonlinear oscillation systems using He’s maxmin method, Frontiers of Mechanical Engineering in China (2011), 2010.
- [18] J. Biazar and F. Mohammadi, Multistep Differential Transform Method for nonlinear oscillators, Nonlinear Sci Lett A 1 (2010), 391–397. Mechanics Research Communications 37 (2010) 111–112.
- [19] J. Fan, He’s frequency–amplitude formulation for the Duffing harmonic Oscillator, Computers and Mathematics with Applications 58 (2009), 2473–2476.
- [20] H. L. Zhang, Application of He’s amplitude–frequency formulation to a nonlinear oscillator with discontinuity, Computers and Mathematics with Applications 58 (2009), 2197–2198.
- [21] A. Beléndez, C. Pascual, D. I. Márquez. T. Beléndez and C. Neipp. Exact solution for the nonlinear pendulum. Revista Brasileira de Ensino de phisica, v. 29 (2007) (4), 645-648.
- [22] N. Herisanu, V. Marinca. A modified variational iterative method for strongly nonlinear oscillators. Nonlinear Sci Lett A. 2010; 1(2): 183–192.
- [23] M. O. Kaya, S. Durmaz, S. A. Demirbag. He’s variational approach to multiple coupled nonlinear oscillators. Int J Non Sci Num Simul. 2010; 11(10): 859–865.
- [24] Y. Khan, A. Mirzabeigy. Improved accuracy of He’s energy balance method for analysis of conservative nonlinear oscillator. Neural Comput Appl. 2014; 25: 889–895.
- [25] A. Khan Naj, A. Ara, A. Khan Nad. On solutions of the nonlinear oscillators by modified homotopy perturbation method. Math Sci Lett. 2014; 3(3): 229–236.
- [26] Y. Khan, M. Akbarzadeb, A. Kargar. Coupling of homotopy and the variational approach for a conservative oscillator with strong odd-nonlinearity. Sci Iran A. 2012; 19(3): 417–422.
- [27] B. S. Wu, C. W. Lim, Y. F. Ma. Analytical approximation to large-amplitude oscillation of a non-linear conservative system. Int J Nonlinear Mech. 2003; 38: 1037–1043.
- [28] J. H. He. The homotopy perturbation method for nonlinear oscillators with discontinuous. Appl Math Comput. 2004; 151: 287–292.
- [29] Belato, D., Weber, H.I., Balthazar, J.M. and Mook, D.T. Chaotic vibrations of a non ideal electro-mechanical system. Internat. J. Solids Structures, 38(10–13), pp. 1699–1706 (2001).
- [30] J. Cai, X. Wu and Y. P. Li. Comparison of multiple scales and KBM methods for strongly nonlinear oscillators with slowly varying parameters, Mech. Res. Comm. 31 (2004) (5), 519–524.
- [31] M. Eissa and M. Sayed. Vibration reduction of a three DOF nonlinear spring pendulum. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) (2), 465–488.
- [32] P. Amore and A. Aranda. Improved Lindstedt-Poincaré method for the solution of nonlinear problems. J. Sound Vib. 283 (2005) (3–5), 1115–1136.
- [33] B. A. Idowu, U. E. Vincent and A. N. Njah. Synchronization of chaos in nonidentical parametrically excited systems. Chaos Solitons Fractals, 39 (2009) (5), 2322–2331.
- [34] T. S. Amera and M. A. Bek. Chaotic responses of a harmonically excited spring pendulum moving in circular path. Nonlinear Anal. RWA, 10 (2009) (5), 3196–3202.
- [35] N. D. Anh, H. Matsuhisa, L. D. Viet and M. Yasuda. Vibration control of an inverted pendulum type structure by passive mass-spring-pendulum dynamic vibration absorber. J. Sound Vib. 307 (2007) (1–2), 187–201.
- [36] A. I. Ovseyevich. The stability of an inverted pendulum when there are rapid random oscillations of the suspension point, J. Appl. Math. Mech. 70(2006) (5), 762–768.
- [37] J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits. Huarjung University Press, Wuuhahn, China, 1986.
- [38] M.G. Sobamowo. Singular perturbation and differential transform methods to two-dimensional flow of nanofluid in a porous channel with expanding/contracting walls subjected to a uniform transverse magnetic field. Thermal Science and Engineering Progress 4 (2017) 71–84.
- [39] S. Ghafoori, M. Motevalli, M.G. Nejad, F. Shakeri, D.D. Ganji, M. Jalaal. Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM. Current Applied Physics 11 (2011) 965-971
- [40] A. Beléndez, E. Arribas, M. Ortuño, S. Gallego, A. Márquez, I. Pascual. Approximate solutions for the nonlinear pendulum equation using a rational harmonic representation. Computers and Mathematics with Applications 64 (2012) 1602–1611.
- [41] A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations. Wiley, New York, 1979.
- [42] T. T. Stephen and J. B. Marion, Classical Dynamics of Particles and Systems, fifth ed. Brook/Cole, Belmont CA, 2004, ISBN 0534408966, (chapter 10).
- [43] Federal Aviation Administration, Pilot’s Encyclopedia of Aeronautical Knowledge. Skyhorse Publishing Inc, Oklahoma City OK, 2007, ISBN 1602390347, Figure 3-21.
- [44] D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, fifth ed. John Wiley & Sons, New York, 1997, ISBN 0471148547, pp. 381.
- [45] G.A. Baker, P. Graves-Morris, Pade Approximants, Cambridge U.P., 1996.

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