Bibliography for Spring Mass Oscillations

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  1. On the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems
    Chen, Der-Wei
    Structural Engineering and Mechanics, v 16, n 3, September, 2003, p 341-360, Compendex.
  2. Integration of dynamic equation of spring-mass-damper systems via Chebyshev polynomials.
    Fallahi, Behrooz; Seif, Mohamed
    Int. J. Comput. Math. 79 (2002), no. 8, 923--930, MathSciNet.  
  3. Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice.
    Friesecke, G.; Theil, F.
    J. Nonlinear Sci. 12 (2002), no. 5, 445--478, MathSciNet.  
  4. An inverse eigenvalue method for frequency isolation in spring-mass systems.
    Egaña, Juan C.; Kuhl, Nelson M.; Santos, Luis C.
    Numer. Linear Algebra Appl. 9 (2002), no. 1, 65--79, MathSciNet.  
  5. Alternative Formulations To Obtain The Eigensolutions Of A Continuous Structure To Which Spring-Mass Systems Are Attached
    Cha P.D.
    Journal of Sound and Vibration, September 2001, vol. 246, no. 4, pp. 741-750(10), Ingenta.
  6. Bending Vibrations Of Beams Coupled By Several Double Spring-Mass Systems
    Inceo G S.; Gürgöze M.
    Journal Of Sound And Vibration, May 2001, Vol. 243, No. 2, Pp. 370-379(10), Ingenta.  
  7. Symmetry Breaking for a System of Two Linear Second-Order Ordinary Differential Equations
    Wafo Soh C.; Mahomed F.M.
    Nonlinear Dynamics, May 2000, vol. 22, no. 1, pp. 121-133(13), Ingenta.
  8. On the numerical reconstruction of a spring-mass system from its natural frequencies.
    Egaña, Juan C.; Soto, Ricardo L.
    Proyecciones 19 (2000), no. 1, 27--41, MathSciNet.  
  9. When and Why Do Water Levels Oscillate in Three Tanks?
    Keith M. Kendig
    Mathematics Magazine: Volume 72, Number 1, 1999, Pages: 22-31.
  10. The Effects of a Stiffening Spring  
    K. E. Clark and S. Hill
    College Math Journal: Volume 30, Number 5, 1999, Pages: 379-382
  11. Inverse Eigenvalue Problem: Existence Of Special Mass-Damper-Spring Systems
    Nylen P.
    Linear Algebra And Its Applications, 1 August 1999, Vol. 297, No. 1, Pp. 107-132(26), MathSciNet.  
  12. Vibration Analysis Of Beams With A Two Degree-Of-Freedom Spring-Mass System
    Chang T.-P.; Chang C.-Y.
    International Journal Of Solids And Structures, February 1998, Vol. 35, No. 5, Pp. 383-401(19), Ingenta.
  13. Concerning the neutron level and the neutron RMS value in a linear feedback model of point reactor kinetics with one group of delayed neutrons and driven by random reactivity noise: application of the Runge-Kutta method to solve a system of stochastic ordinary differential equations
    Behringer K.
    Annals of Nuclear Energy, July 1998, vol. 25, no. 11, pp. 801-820(20), Ingenta.
  14. Inverse Eigenvalue Problem: Existence Of Special Spring - Mass Systems
    Nylen P.; Uhlig F.
    Inverse Problems, 1997, Vol. 13, No. 4, Pp. 1071-1081(11), MathSciNet.  
  15. Probabilistic interpretation of a system of semi-linear parabolic partial differential equations
    Pardoux E.; Pradeilles F.; Rao Z.
    Annales de l'Institut Henri Poincare (B) Probability and Statistics, 1997, vol. 33, no. 4, pp. 467-490(24), Ingenta.
  16. Inverse eigenvalue problems associated with spring-mass systems.
    Nylen, Peter; Uhlig, Frank
    Proceedings of the Fifth Conference of the International Linear Algebra Society (Atlanta, GA, 1995). Linear Algebra Appl. 254 (1997), 409--425, MathSciNet.  
  17. Geometric Properties of Factorable Planar Systems of Differential Equations (in Classroom Notes)  
    Hassan Sedaghat  
    SIAM Review, Vol. 38, No. 4. (Dec., 1996), pp. 660-665, Jstor.  
  18. Analysis Of Free Vibration Of Rotating Disk -Blade Coupled Systems By Using Artificial Springs And Orthogonal Polynomials
    Tomioka T.; Kobayashi Y.; Yamada G.
    Journal of Sound and Vibration, March 1996, vol. 191, no. 1, pp. 53-73(21), Ingenta.
  19. Dynamics of two spring-connected masses in orbit.
    Wang, Li-Sheng; Cheng, Shyh-Feng
    Celestial Mech. Dynam. Astronom. 63 (1995/96), no. 3-4, 289--312, MathSciNet.  
  20. Distinguished Oscillations of a Forced Harmonic Oscillator
    T. G. Proctor
    College Math Journal: Volume 26, Number 2, 1995, Pages: 111-117.  
  21. On Isospectral Spring-Mass Systems
    Gladwell G.M.L.
    Inverse Problems, 1995, Vol. 11, No. 3, Pp. 591-602(12), MathSciNet.  
  22. Robust end point tracking control of a two-degree-of-freedom mass-spring-damper system.
    Bridges, M. M.; Zhu, J. Y.; Dawson, D. M.; Qu, Z.
    Internat. J. Control 59 (1994), no. 5, 1309--1324, MathSciNet.  
  23. A numerical homotopy method and investigations of a spring-mass system.
    Davidson, B. D.; Stewart, D. E.
    Math. Models Methods Appl. Sci. 3 (1993), no. 3, 395--416, MathSciNet.  
  24. Physical Parameters Reconstruction of a Free-Free Mass-Spring System from Its Spectra  
    Yitshak M. Ram, James Caldwell  
    SIAM Journal on Applied Mathematics, Vol. 52, No. 1. (Feb., 1992), pp. 140-152, Jstor.  
  25. Forced Transverse Oscillations in a Simple Spring-Mass System  
    Lawrence K. Forbes  
    SIAM Journal on Applied Mathematics, Vol. 51, No. 5. (Oct., 1991), pp. 1380-1396, Jstor.  
  26. A Series Analysis of Forced Transverse Oscillations in a Spring-Mass System  
    Lawrence K. Forbes  
    SIAM Journal on Applied Mathematics, Vol. 49, No. 3. (Jun., 1989), pp. 704-719, Jstor.  
  27. Quasicontinuous spatial motion of a mass-spring chain.
    Rosenau, Philip
    Phys. D 27 (1987), no. 1-2, 224--234, MathSciNet.  
  28. Dynamics of nonlinear mass-spring chains near the continuum limit.
    Rosenau, Philip
    Phys. Lett. A 118 (1986), no. 5, 222--227, MathSciNet.  
  29. Periodic and chaotic motions of a mass-spring system under harmonic force.
    Bapat, C. N.; Sankar, S.
    J. Sound Vibration 108 (1986), no. 3, 533--536, MathSciNet.  
  30. Systems of Differential Equations Subject to Mild Integral Conditions  
    William F. Trench  
    Proceedings of the American Mathematical Society, Vol. 87, No. 2. (Feb., 1983), pp. 263-270, Jstor.  
  31. Mass-Spring System With Singular Control.
    Abdelkader, Mostafa A.  
    International Journal of Control, v 35, n 2, Feb, 1982, p 281-289, Compendex.
  32. The Spring and Mass Pendulum: An Exercise in Mathematical Modeling
    Mills, David S.
    Physics Teacher v19 n6 p404-05 Sep 1981
  33. Computational Complexity of One-Step Methods for Systems of Differential Equations  
    Arthur G. Werschulz  
    Mathematics of Computation, Vol. 34, No. 149. (Jan., 1980), pp. 155-174, Jstor.  
  34. Deceptively Simple Harmonic Motion: A Mass on a Spiral Spring  
    McDonald, F.
    American Journal of Physics v48 n3 p189-92 Mar 1980
  35. Distribution of Eigenvalues of A Two-Parameter System of Differential Equations  
    M. Faierman  
    Transactions of the American Mathematical Society, Vol. 247. (Jan., 1979), pp. 45-86, Jstor.  
  36. An Asymptotic Solution of a Nonhomogeneous Linear System of Differential Equations  
    Thomas G. Hallam  
    Proceedings of the American Mathematical Society, Vol. 29, No. 3. (Aug., 1971), pp. 529-534, Jstor.  
  37. Weakly Bounded Systems of Differential Equations  
    Thomas G. Hallam  
    Proceedings of the American Mathematical Society, Vol. 19, No. 5. (Oct., 1968), pp. 1242-1246, Jstor.  
  38. Asymptotic Methods for Systems of Differential Equations in which Some Variables Have Very Short Response Times  
    D. B. MacMillan  
    SIAM Journal on Applied Mathematics, Vol. 16, No. 4. (Jul., 1968), pp. 704-722, Jstor.  
  39. A Note on the Characteristic Numbers of Linear Systems of Differential-Difference Equations  
    John Abramowich  
    Proceedings of the American Mathematical Society, Vol. 19, No. 1. (Feb., 1968), pp. 50-54, Jstor.  
  40. Linear Systems of Differential Equations with Periodic Solutions  
    James S. Muldowney  
    Proceedings of the American Mathematical Society, Vol. 18, No. 1. (Feb., 1967), pp. 22-27, Jstor.  
  41. Asymptotic Almost Periodicity of Solutions of a System of Differential Equations  
    W. R. Utz, Paul Waltman  
    Proceedings of the American Mathematical Society, Vol. 18, No. 4. (Aug., 1967), pp. 597-601, Jstor.  
  42. Exponential Solutions of Linear Systems of Differential Equations whose Coefficient Matrix is Skew Symmetric  
    Irving J. Epstein  
    Proceedings of the American Mathematical Society, Vol. 17, No. 1. (Feb., 1966), pp. 48-54, Jstor.  
  43. Periodic Solutions of Systems of Differential Equations  
    Irving J. Epstein  
    Proceedings of the American Mathematical Society, Vol. 13, No. 5. (Oct., 1962), pp. 690-694, Jstor.  
  44. Systems of Differential Equations without Linear Terms   
    Courtney Coleman  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 47, No. 10. (Oct. 15, 1961), pp. 1650-1651, Jstor.  
  45. The design of a computer program to determine the natural frequencies and normal modes of vibration of an in-line mechanical system of springs and masses.
    O'Callaghan, T.
    J. Soc. Indust. Appl. Math. 9 1961 294--310, MathSciNet.  
  46. On the Simultaneous Determination of Several Eigensolutions of a Self-Adjoint System of Differential Equations  
    P. Laasonen  
    Mathematical Tables and Other Aids to Computation, Vol. 13, No. 65. (Jan., 1959), pp. 13-20, Jstor.  
  47. Min-max solutions for the linear mass-spring system.
    Sevin, Eugene
    J. Appl. Mech. 24 (1957), 131--136, MathSciNet.  
  48. Forced Periodic Solutions of Systems of Differential Equations  
    H. A. Antosiewicz  
    The Annals of Mathematics, 2nd Ser., Vol. 57, No. 2. (Mar., 1953), pp. 314-317, Jstor.  
  49. Vibration of a beam with concentrated mass, spring, and dashpot.
    Young, Dana
    J. Appl. Mech. 15, (1948). 65--72, MathSciNet.  
  50. On the Stability of Systems of Differential Equations  
    Richard Bellman  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 32, No. 6. (Jun. 15, 1946), pp. 190-193, Jstor.  
  51. Forced and free motion of a mass on an air spring.
    Sussholz, B.
    J. Appl. Mech. 11, (1944). A-101--A-107, MathSciNet.  
  52. Systems of Differential Equations. I. Theory of Ideal  
    J. F. Ritt  
    American Journal of Mathematics, Vol. 60, No. 3. (Jul., 1938), pp. 535-548, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004