Coupled oscillators and pendula

Resources

References

Journal papers

Altshuler, E. and R. Garcia (2003), "Josephson junctions in a magnetic field: insights from coupled pendula," Am. J. Phys. 71 (4), 405-408.

Bender, P. A. (1985), "A fascinating resonant double pendulum," Am. J. Phys. 53, 1114.

Benenson, R. E. and B. B. Marsh (1988), "Coupled oscillations of a ball and a curve-track pendulum," Am. J. Phys. 56 (4), 345-8.

Berg, R. E. (1991), "Pendulum waves: a demonstration of wave motion using pendula," Am. J. Phys. 59, 186-187.

Berg, R., E. and T. S. Marshall (1991), "Wilberforce pendulum oscillations and normal modes," Am. J. Phys. 59, 32-38.

Blair, J. M. (1971), "Laboratory experiments involving the two-mode analysis of coupled oscillators," Am. J. Phys. 39, 555-557.

Cross, R. (2005), "A double pendulum swing experiment: in search of a better bat," Am. J. Phys. 73 (4), 330-9.

Curzon, F. L. (1984), "Classroom simulation of the coupled motion of piano strings," Am. J. Phys. 52, 137-139.

Davidovic, D. M., B. A. Anicin, and V. M. Babovic (1996), "The libration limits of the elastic pendulum," Am. J. Phys. 64 (3), 338-42.

Dobrovolskis, A. (1973), "Rubber band pendulum," Am. J. Phys. 41, 1103-1106.

Karioris, F. G. and K. S. Mendelson (1992), "A novel coupled oscillation demonstration," Am. J. Phys. 60, 508-513.

Köpf, U. (1990), "Wilberforce's pendulum revisited," Am. J. Phys. 58 (9), 833-7.

Lama, W. L., R. Jodoin, and L. Mandel (1972), "Superradiance in radiatively coupled tuning forks," Am. J. Phys. 40, 32-37.

Lee, S. M. (1970), "The double-simple pendulum problem," Am. J. Phys. 38, 536-537.

Levinson, D. A. (1977), "Natural frequencies of a spherical compound pendulum," Am. J. Phys. 45, 579.

McKibben, J. L. (1977), "Triple pendulum as an analog to three coupled stationary states," Am. J. Phys. 45, 1022-1026.

Moloney, M. J. (1978), "String-coupled pendulum oscillators: theory and experiment," Am. J. Phys. 46, 1245-1246.

Pedersen, N. F. and O. Soerensen, Hoffmann (1977), "The compound pendulum in intermediate laboratories and demonstrations," Am. J. Phys. 45, 994-998.

Romer, R. H. (1970), "A double pendulum "art machine"," Am. J. Phys. 38, 1116-1121.

Rusbridge, M. G. (1980), "Motion of the sprung pendulum," Am. J. Phys. 48, 146-151.

Shinbrot, T., C. Grebogi, J. Wisdom, and J. A. Yorke (1992), "Chaos in a double pendulum," Am. J. Phys. 60, 491-499.

Spencer, R. L. and R. D. Robertson (2001), "Mode detuning in systems of weakly coupled oscillators," Am. J. Phys. 69 (11), 1191-7.

Wallach, D. L. and et. al. (1988), "The effect of mass of the center spring in one-dimensional coupled harmonic oscillators," Am. J. Phys. 56 (12), 1120-3.

Weigman, B. J. and H. F. Perry (1993), "Experimental determination of normal frequencies in coupled mechanical oscillator systems using fast Fourier transforms: an advanced undergraduate laboratory," Am. J. Phys. 61 (11), 1022-7.

Husman, M., L. Schwieters, M., and H. Rabitz (1991), "Molecular-dynamics simulator for optimal control of molecular motion," Am. J. Phys. 59, 1012-1017.

Diaz-de-Anda, A., K. Volke-Sepulveda, J. Flores, C. Sanchez-Perez, and L. Gutierrez (2015), "Study of coupled resonators in analogous wave systems: mechanical, elastic, and optical," Am. J. Phys. 83 (12), 1012 - 18.

Hubner, M. and J. Kroger (2018), "Experimental verification of the adiabatic transfer in Wilberforce pendulum normal modes," Am. J. Phys. 86, 818 - 24.Liang, C., W. Ke, M. Fu, C. Wang, and X. Chen (2015), "An undergraduate experiment of wave motion using a coupled-pendulum chain," Am. J. Phys. 83 (5), 389 - 94.

Lockhart, A. B., A. Skinner, W. Newman, D. B. Steinwachs, and S. A. Hilbert (2018), "An experimental demonstration of avoided crossings with masses on springs," Am. J. Phys. 86 (7), 526 - 30.

Newman, W., A. Skinner, and S. A. Hilbert (2017), "An acoustic demonstration of an avoided crossing," Am. J. Phys. 85 (11), 844 - 9.

Virgin, L. N. (2018), "Sympathetic resonance," Am. J. Phys. 86 (6), 439 - 42.

Debowska, E., S. Jakubowicz, and Z. Mazur (1999), "Computer visualization of the beating of a Wilberforce pendulum," Eur. J. Phys. 20(2), 89-95.

Greczylo, T. and E. Debowska (2002), "Using a digital video camera to examine coupled oscillations," Eur. J. Phys. 23 (4), 441-7.

Levesque, L. (2006), "Revisiting the coupled-mass system and analogy with a simple band gap structure," Eur. J. Phys. 27 (1), 133-45.

Monsoriu, J. A., M. H. Gimenez, J. Riera, and A. Vidaurre (2005), "Measuring coupled oscillations using an automated video analysis technique based on image recognition," Eur. J. Phys. 26 (6), 1149-55.

Silva, R. S., Jr., O. S. Silva, Jr., and M. S. R. Miltao, "Adiabatic invariants of two pendulums coupled by a spring," Eur. J. Phys. (UK) 40(4), 045001 (8 pp.) .

Castro-Palacio, J. C., L. Velazquez-Abad, F. Gimenez, and J. A. Monsoriu (2013), "A Quantitative Analysis of Coupled Oscillations Using Mobile Accelerometer Sensors," Eur. J. Phys. (UK) 34 (3), 737 - 44.

Dolinko, A. E. (2009), "From Newton's second law to Huygens's principle: visualizing waves in a large array of masses joined by springs," Eur. J. Phys. (UK) 30 (6), 1217 - 28.

Donoso, G., C. L. Ladera, and P. Martin (2010), "Magnetically coupled magnet-spring oscillators," Eur. J. Phys. (UK) 31 (3), 433 - 52.

Hu, Q., W. Liu, H. Yang, J. Xiao, and X. Qian (2013), "Experimental study on synchronization of three coupled mechanical metronomes," Eur. J. Phys. (UK) 34, 291 - 302.Leroy, V., J. -C. Bacri, T. Hocquet, and M. Devaud (2006), "Simulating a one-half spin with two coupled pendula: the free Larmor precession," Eur. J. Phys. (UK) 27 (6), 1363 - 83.

Leroy, V., J. -C. Bacri, T. Hocquet, and M. Devaud (2010), "Simulating a one-half spin with two coupled pendula: II. The parametrically induced Rabi precession," Eur. J. Phys. (UK) 31 (1), 157 - 70.

Li, A., J. Zeng, H. Yang, and J. Xiao (2011), "A Laboratory Experiment on Coupled Non-identical Pendulums," Eur. J. Phys. (UK) 32 (5), 1251 - 7.

Radomirovic, D. and I. Kovacic (2015), "Stiffness properties of certain oscillatory systems: quantification and possibilities for corrections," Eur. J. Phys. (UK) 36 (3), 035031 (15 pp.) .

Rador, T. (2016), "A tale of two oscillators," Eur. J. Phys. (UK) 37 (4), 045006 (7 pp.) .

Sans, J. A., F. J. Manjon, A. L. J. Pereira, J. A. Gomez-Tejedor, and J. A. Monsoriu (2013), "Oscillations studied with the smartphone ambient light sensor," Eur. J. Phys. (UK) 34 (6), 1349 - 54.

Satpathy, S., A. Roy, and A. Mohapatra (2012), "Fano interference in classical oscillators," Eur. J. Phys. (UK) 33 (4), 863 - 71.

Silva, J. P. and A. J. Silvestre (2008), "Surprises of the transformer as a coupled oscillator system," Eur. J. Phys. (UK) 29 (3), 413 - 20.

Yang, J., Y. Wang, Y. Yizhen, J. Xiao, and X. Wang (2018), "Huygens' synchronization experiment revisited: luck or skill?," Eur. J. Phys. (UK) 39 (5), 055004 (14 pp.) .

Zhu, C., J. Lei, Y. Wu, N. Li, D. Chen, and Q. Shi (2015), "Experimental observation of solitary waves in a new designed pendulum chain system," Eur. J. Phys. (UK) 36 (4), 045002 (10 pp.) .

Bachman, C. H. (1976), "Some observations on the process of walking," Phys. Teach. 14 (6), 360-2.

Chagnon, P. (1992), "Animated displays: coupled mechanical oscillators," Phys. Teach. 30, 275-279.

Giles, M. M. (1974), "A resonance demonstration," Phys. Teach. 12 (3), 178-9.

Hinrichsen, P. F. (1981), "Practical applications of the compound pendulum," Phys. Teach. 19 (5), 286-92.

Minnix, R. B. and D. R. Carpenter, Jr. (1984), "Collision balls and coupled pendulums for the overhead projector," Phys. Teach. 22 (4), 258-9.

Pierrus, J. and M. M. Michaelis (1980), "Demonstration of coupled oscillations using permanent magnets," Phys. Teach. 18 (1)

Priest, J. and J. Poth (1982), "Teaching physics with coupled pendulums," Phys. Teach. 20 (2), 80-5.

Richards, D. A. (1981), "Coupled oscillations," Phys. Educ. 16, 83.

Monteiro, M., C. Stari, C. Cabeza, and A. C. Martiacute (2020), "Experimental analysis of a compound pendulum with variable suspension point," Phys. Educ. 55 (2), 023004 (4 pp.) .