Simple pendulum

Resources

Lab manuals

Oscillations experiments with undamped and damped pendulum (lab manual – Bridgewater College and college of Wooster – Deva O’Neill and Susan Lehman)

References

Journal papers

Abdel-Rahman, A-M. M. (1983), "The simple pendulum in a rotating frame," AJP 51, 721-724.

Araki, T. (1994), "Measurement of simple pendulum motion using flux-gate magnetometer," Am. J. Phys. 62 (6), 569-571.

Armstrong, H. L. (1976), "Effect of the mass of the cord on the period of a simple pendulum," AJP 44, 564-566.

Asano, K. (1975), "On the theory of an electrostatic pendulum oscillator," AJP 43, 423-427.

Basano, L. and P. Ottonello (1991), "Digital pendulum damping: the single-oscillation approach," AJP 59, 1018-1023.

Basano, L., P. Ottonello, and V. Palestini (1996), "Ripples in the energy of a damped oscillator: the experimental point of view," Am. J. Phys. 64 (10), 1326-1329.

Bazin, M. and P. Lucie (1981), "The pendulum reborn: time measurements in the teaching laboratory," AJP 49, 758-761.

Blitzer, L. (1965), "Inverted pendulum," Am. J. Phys. 33, 1076-1078.

Bulur, E., S. O. Anilturk, and A. M. Ozer (1996), "Computer analysis of pendulum motion: an alternative way of collecting experimental data," Am. J. Phys. 64 (10), 1333-1337.

Cadwell, L. H. and E. R. Boyko (1991), "Linearization of the simple pendulum," AJP 59, 979-981.

Candela, D., K. M. Martini, R. V. Krotkov, and K. H. Langley (2001), "Bessel's improved Kater pendulum in the teaching lab," Am. J. Phys. 69 (6), 714-20.

Crawford, F. S. (1975), "Damping of a simple pendulum," AJP 43, 276-277.

Crowell, A. D. (1981), "Motion of the Earth as viewed from the moon and the y-suspended pendulum," AJP 49, 452-454.

Dix, F. (1975), "A pendulum counter-timer using a photocell gate," AJP 43, 280.

Dolfo, G. and J. Vigue (2015), "A more accurate theory of a flexible-beam pendulum," Am. J. Phys. 83 (6), 525 - 30.

Epstein, S. T. and M. G. Olsson (1977), "Comment on "Effect of the mass of the cord on the period of a simple pendulum" [H. L. Armostrong, Am. J. Phys. 44, 564 (1976)]," AJP 45, 672-673.

Falco, C. M. (1976), "Phase-space of a driven, damped pendulum (Josephson weak link)," AJP 44, 733-740.

Fulcher, L. P. and B. F. Davis (1976), "Theoretical and experimental study of the motion of the simple pendulum," AJP 44, 51-55.

Ganley, W. P. (1985), " SImple pendulum approximation," AJP 53, 73-76.

Gil, S. and D. E. Di Gregorio (2003), "Nonisochronism in the interrupted pendulum," Am. J. Phys. 71 (11), 1115-20.

Giltinan, D. A., D. L. Wagner, and T. A. Walkiewicz (1996), "The physical pendulum on a cylindrical support," Am. J. Phys. 64 (2), 144-6.

Gleiser, R. J. (1979), "Small amplitude oscillations of a quasi-ideal pendulum," AJP 47, 640-643.

Greenslade, T. B., Jr. and A. J. Owens (1980), "Reconstructed nineteenth-century experiment with physical pendula," AJP 48, 487-488.

Greenwood, M. S. (1987), "Using videotapes to study underdamped motion of a pendulum: a laboratory project," AJP 55, 645-648.

Hall, D. E. (1981), "Comments on Fourier analysis of the simple pendulum," AJP 49, 792.

Haque-Copilah, S. (1996), "Extremely simple demonstration of forced oscillation," Am. J. Phys. 64 (4), 507-8.

Helrich, C. and T. Lehman (1979), "A rolling pendulum bob: conservation of energy and partitioning of kinetic energy," AJP 47, 367-368.

Hoyng, P. (2014), "Dynamics and performance of clock pendulums," Am. J. Phys. 82, 1053 - 61.Hugo, V. and B. R. Childers (1983), "Magnetic pendulum apparatus for analog demonstration of first-order and second-order phase transitions and tricritical points," AJP 51, 39-43.

Isenor, N. R. (1969), "Mechanical model of a q-switched laser," AJP 37, 1159-1160.

Jesse, K. E. (1980), "Kater pendulum modification," AJP 48, 785-786.

Kettler, J. E. (1995), "A variable mass physical pendulum," Am. J. Phys. 63 (11), 1049-51.

Klein, W. and P. Mittelstaedt (1997), "A simple experimental demonstration of the principle of equivalence," Am. J. Phys. 65 (4), 316-20.

Kwasnoski, J. B. and R. S. Murphy (1984), "The classic pendulum experiment - on Jupiter or Saturn," AJP 52, 85.

Köpf, U. (1990), "Wilberforce's pendulum revisited," AJP 58, 833-7.

Levy-Leblond, J. (1978), "Rock or roll: non-isochronous small oscillations (an example)," AJP 46, 106-107.

Livesey, D. L. (1987), "The precession of simple pendulum orbits," AJP 55, 618-621.

Marschall, L. A. (1981), "Driven "portulum": a rolling ball as a simple oscillating system," AJP 49, 557-561.

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

McNeill, D. J. (1965), "A simple low-frequency current source," AJP 33, 964-965.

Miller, B. J. (1974), "More realistic treatment of the simple pendulum without difficult mathematics," AJP 42, 298-303.

Mills, D. S. (1980), "The physical pendulum: a computer-augmented laboratory exercise," AJP 48, 314-316.

Mires, R. W. and R. D. Peters (1994), "Motion of a leaky pendulum," Am. J. Phys. 62 (2), 137-9.

Montgomery, C. G. (1978), "Pendulum on a massive cord," AJP 46, 411-412.

Nelson, R. A. and M. G. Olsson (1986), "The pendulum - rich physics from a simple system," AJP 54, 112-21.

Nicklin, R. C. (1985), "Erratum: "The digital pendulum" [Am. J. Phys. 52, 632 (1984)]," AJP 53.

Nicklin, R. C. and J. B. Rafert (1984), "The digital pendulum," AJP 52, 632-639.

Ochoa, O. R. and N. F. Kolp (1997), "The computer mouse as a data acquisition interface: application to harmonic oscillators," Am. J. Phys. 65 (11), 1115-18.

Peters, R. D. and J. A. Shepherd (1989), "A pendulum with adjustable trends in period," AJP 57, 535-9.

Priest, J. (1986), "Interfacing pendulums to a microcomputer," AJP 54, 953-5.

Quist, G. M. (1983), "The PET and pendulum: an application of microcomputers to the undergraduate laboratory," AJP 51, 145-149.

Randazzo, J. M., S. A. Ibanez, and J. M. Rossello (2018), "An asymmetric isochronous pendulum," Am. J. Phys. 86 (7), 518 - 25.

Sachs, A. (1976), "Blackwood pendulum experiment revisited," AJP 44, 182-183.

Schmidt, V. H. and B. R. Childers (1984), "Magnetic pendulum apparatus for analog demonstration of first-order and second-order phase transitions and tricritical points," AJP 52, 39-43.

Sheppard, D. MN. (1970), "Using one pendulum and a rotating mass to measure the universal gravitational constant," AJP 38, 380.

Squire, P. T. (1986), "Pendulum damping," AJP 54, 984-991.

Then, J. W. (1965), "Bifilar pendulum - an experimental study for the advanced laboratory," AJP 33, 545-547.

Then, J. W. and K. Chang (1970), "Experimental determination of moments of inertia by the bifilar pendulum method," AJP 38, 537-539.

Wagner, D. L., T. A. Walkiewicz, and D. A. Giltinan (1995), "The partial ring pendulum," Am. J. Phys. 63 (11), 1014-17.

Weigel, C., J. M. Wachter, P. Wagoner, and T. J. Atherton (2016), "Predicting the influence of plate geometry on the eddy-current pendulum," Am. J. Phys. 84 (9), 653 - 63.

Whitaker, R. J. (2001), "Harmonographs. I. Pendulum design," Am. J. Phys. 69 (2), 162-73.

Wickramasinghe, T. and R. Ochoa (2005), "Analysis of the linearity of half periods of the Lorentz pendulum," Am. J. Phys. 73 (5), 442-5.

Wikening, G. and J. Hesse (1981), "Electrical pendulum for educational purpose," AJP 49, 90-91.

Yorke, E. D. (1978), "Square-wave model for a pendulum with an oscillating suspension," AJP 46, 285-288.

Aggarwal, N., N. Verma, and P. Arun (2005), "Simple pendulum revisited," Eur. J. Phys. 26 (3), 517-23.

Anicin, B., D. M. Davidovic, and V. M. Babovic (1993), "On the linear theory of the elastic pendulum," EJP 14, 132-135.

Bacon, M. E. and Do Dai Nguyen (2005), "Real-world damping of a physical pendulum," Eur. J. Phys. 26 (4), 651-5.

Bellomonte, L., I. Guastella, and R. M. Sperandeo-Mineo (2005), "Mechanical models of amplitude and frequency modulation," Eur. J. Phys. 26 (3), 409-22.

Butikov, E. I. (1999), "The rigid pendulum-an antique but evergreen physical model," Eur. J. Phys. 20 (6), 429-41.

Crook, A. W. (2001), "A tale of a clock," Eur. J. Phys. 22 (5), 549-60.

Delcour, J. and L. Hoffenbom (1988), "Mesure de temps par ordinateur," EJP 9, 135-138.

Di Lieto, A., S. Fenicia, and P. Mancini (1991), "A computer assisted pendulum for didactics," EJP 12, 51-52.

Doménech, A. and T. Doménech (1988), "Relationships between the scattering angles in pendulum collisions," EJP 9, 116-122.

Gonzalez, M. I. and A. Bol (2006), "Controlled damping of a physical pendulum: experiments near critical conditions," Eur. J. Phys. 27(2), 257-64.

Gough, W. (1983), "The period of a simple pendulum is not 2*pi*(L/g)**1/2," EJP 4, 53-54.

Peters, R. D. (1997), "Automated Kater pendulum," Eur. J. Phys. 18 (3), 217-21.

Xiao-jun Wang, C. Schmitt, and M. Payne (2002), "Oscillations with three damping effects," Eur. J. Phys. 23 (2), 155-64.

Yoshida, S. and T. Findley (2005), "Analysis of a simple pendulum driven at its suspension point," Eur. J. Phys. 26 (3), 493-9.

Zonetti, L. F. C., A. S. S. Camargo, J. Sartori, D. F. de Sousa, and L. A. O. Nunes (1999), "A demonstration of dry and viscous damping of an oscillating pendulum," Eur. J. Phys. 20 (2), 85-8.

Arun, P. (2010), "The moving centre of mass of a leaking bob," Eur. J. Phys. (UK) 31 (4), 811 - 18.

Bel, A., W. Reartes, and A. Torresi (2012), "Global study of the simple pendulum by the homotopy analysis method," Eur. J. Phys. (UK) 33 (2), 231 - 41.

Belendez, A., E. Arribas, A. Marquez, M. Ortuno, and S. Gallego (2011), "Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion," Eur. J. Phys. (UK) 32 (5), 1303 - 10.

Belendez, A., J. Frances, M. Ortuno, S. Gallego, and J. G. Bernabeu (2010), "Higher accurate approximate solutions for the simple pendulum in terms of elementary functions," Eur. J. Phys. (UK) 31 (3), L65 - L70 -.

Caccamo, M. T. and S. Magazu (2017), "Variable mass pendulum behaviour processed by wavelet analysis," Eur. J. Phys. (UK) 38 (1), 015804 (9 pp.) .

Dolfo, G., D. Castex, and J. Vigue (2016), "Damping mechanisms of a pendulum," Eur. J. Phys. (UK) 37 (6), 065004 (16 pp.) .

Fernandes, J. C., P. J. Sebastiao, L. N. Goncalves, and A. Ferraz (2017), "Study of large-angle anharmonic oscillations of a physical pendulum using an acceleration sensor," Eur. J. Phys. (UK) 38 (4), 045004 (18 pp.) .

Gonzalez, M. I. and A. Bol (2006), "Controlled damping of a physical pendulum: experiments near critical conditions," Eur. J. Phys. (UK) 27 (2), 257 - 64.

Gurri, P., D. Amat, J. Espar, J. Puig, G. Jimenez, L. Sendra, and L. C. Pardo (2017), "Pendulum dynamics in an amusement park," Eur. J. Phys. (UK) 38 (3), 035005 (9 pp.) .

Hou, Z., K. Yuan, F. Xie, H. Jin, and Q. Shi (2015), "Oscillation properties of a simple pendulum in a viscous liquid," Eur. J. Phys. (UK) 36, 015011 (8 pp.) .Johannessen, K. (2010), "An approximate solution to the equation of motion for large-angle oscillations of the simple pendulum with initial velocity," Eur. J. Phys. (UK) 31 (3), 511 - 18.

Johannessen, K. (2014), "An analytical solution to the equation of motion for the damped nonlinear pendulum," Eur. J. Phys. (UK) 35 (3), 035014 (13 pp.) .

Kharkongor, D. and M. C. Mahato (2018), "Resonance oscillation of a damped driven simple pendulum," Eur. J. Phys. (UK) 39 (6), 065002 (10 pp.) .

Kladivova, M. and L. Mucha (2014), "Physical pendulum-a simple experiment can give comprehensive information about a rigid body," Eur. J. Phys. (UK) 35 (2), 025018 (14 pp.) .

Kraftmakher, Y. (2007), "Experiments with a magnetically controlled pendulum," Eur. J. Phys. (UK) 28 (5), 1007 - 20.

Monteiro, M., C. Cabeza, and A. C. Marti (2014), "Exploring phase space using smartphone acceleration and rotation sensors simultaneously," Eur. J. Phys. (UK) 35 (4), 045013 (9 pp.) .

Lima, F. M. S. (2009), "A trigonometric approximation for the tension in the string of a simple pendulum accurate for all amplitudes," Eur. J. Phys. (UK) 30 (6), L95 - L102 -.

Lima, F. M. S. (2008), "Simple `log formulae' for pendulum motion valid for any amplitude," Eur. J. Phys. (UK) 29 (5), 1091 - 8.

Lira, I. (2007), "Introducing scale analysis by way of a pendulum," Eur. J. Phys. (UK) 28 (2), 289 - 99.

Llibre, J. and M. A. Teixeira (2010), "On the stable limit cycle of a weight-driven pendulum clock," Eur. J. Phys. (UK) 31 (5), 1249 - 54.

Malgieri, M., P. Onorato, P. Mascheretti, and A. De Ambrosis (2016), "Two experiments for the measurement of the centre of percussion of a physical pendulum," Eur. J. Phys. (UK) 37 (5), 055002 (16 pp.) .

Mungan, C. E. and T. C. Lipscombe (2013), "Oscillations of a quadratically damped pendulum," Eur. J. Phys. (UK) 34 (5), 1243 - 53.

Qing-Xin, Y. and D. Pei (2009), "Comment on `approximation for a large-angle simple pendulum period'," Eur. J. Phys. (UK) 30 (5), L79 - L82 -.

Qing-Xin, Y. and D. Pei (2010), "Note on the `log formulae' for pendulum motion valid for any amplitude," Eur. J. Phys. (UK) 31 (1), L15 - L16 -.

Quiroga, G. D. and P. A. Ospina-Henao (2017), "Dynamics of damped oscillations: physical pendulum," Eur. J. Phys. (UK) 38 (6), 065005 (14 pp.) .

Qureshi, M. I., M. Rafat, and S. I. Azad (2010), "The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach," Eur. J. Phys. (UK) 31 (6), 1485 - 97.

Shima, H. (2012), "How far can Tarzan jump?," Eur. J. Phys. (UK) 33 (6), 1687 - 93.

Turkyilmazoglu, M. (2010), "Improvements in the approximate formulae for the period of the simple pendulum," Eur. J. Phys. (UK) 31 (5), 1007 - 11.

Yang, T., B. Fang, S. Li, and W. Huang (2010), "Explicit analytical solution of a pendulum with periodically varying length," Eur. J. Phys. (UK) 31 (5), 1089 - 96.

Arons, A. B. (1977), "How long is a simple pendulum? [student experiment]," Phys. Teach. 15 (5), 300-1.

Hageseth, G. T. (1987), "The liquid pendulum," Phys. Teach. 25 (7), 427.

Phelps, F. M., IV, F. M. Phelps, III, and J. Gormley (1980), "An experiment that excited high school physics students [pendulum oscillation, statistical analysis]," Phys. Teach. 18 (1), 48-9.

Hennig, L. A. A. (1975), "Variable g pendulum, an evaluation," Phys. Teach. 13 (6), 365.

Furtak, T. E. (1975), "Digital electronic pendulum monitor [student experiment]," Phys. Teach. 13 (5), 309-10.

Hewson, P. W., S. Jaunich, and M. H. Moreton (1979), "An accurate direct reading accelerometer," Phys. Teach. 17 (1), 45-7.

Santarelli, V., J. Carolla, and M. Ferner (1993), "A new look at the simple pendulum," PT 31, 236-237.

Taylor, K. N. (1983), "Tinker toys have their moments of inertia," Phys. Teach. 21 (7), 456-8.

Alho, J., H. Silva, V. Teodoro, and G. Bonfait (2019), "A simple pendulum studied with a low-cost wireless acquisition board," Phys. Educ. (UK) 54 (1), 015015 (12 pp.) .

Boving, R., J. Helleman, and R. De Wilde (1983), "Teaching damped and forced oscillations in the student laboratory," PE 18, 275-276.

French, M. M. J. (2019), "Building a bowling ball pendulum," Phys. Educ. (UK) 54 (3), 033003 (2 pp.) .

Madrid, A. C. (1983), "The period of a pendulum," PE 18, 271-272.

Pili, U. B. (2020), "Modeling damped oscillations of a simple pendulum due to magnetic braking," Phys. Educ. 55 (3), 035025 (5 pp.) .

Pili, U. B. (2020), "Sound-based measurement of g using a door alarm and a smartphone: listening to the simple pendulum," Phys. Educ. 55 (3), 033001 (4 pp.) .

Pili, U. and R. Violanda (2019), "Measurement of the gravitational acceleration using a simple pendulum apparatus, ultrasonic sensor, and Arduino," Phys. Educ. (UK) 54 (4), 043009 (5 pp.) .

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