Synchronization of Huygens' Clocks: An Elementary Treatment

POSTER

Abstract

Huygens proposed a general model to explain the synchronization of two oscillators. We describe synchronization of two pendulums mounted on a cart. The cart moves along the horizontal: the motion is damped. We show that the principle of conservation of momentum can be used to describe an escapement mechanism. Simple graphical methods are used to show that the motion of the two pendulums can be described in terms of a symmetric and anti-symmetric ``mode.' We quantify the damping of the pendulums and show that the two modes are described by two different damping constants. We discuss that this property explains why only the anti-symmetric mode ``survives'' for long time; i.e., the two pendulums are synchronized. We discuss direction for future investigation.

Authors

  • Ulrich Zurcher

    Physics Dept, Cleveland State University

  • Frazier Baker

    Youngstown State University, Kent State University, Liquid Crystal Institute, Kent State University, Department of Biological Sciences, Kent State University, Department of Physics, Department of Chemistry and Biochemistry, Kent State University, Stony Brook Univ, Ohio Univ, Institute for Advanced Simulation, Institut fur Kernphysik, and Julich Center, Bowling Green State University, Dept. of Physics, Hiram College, Ohio State Univ - Columbus, Kent State University, Psychology Dept, Cleveland State University, Physics Dept, Cleveland State University, Chemical Physics Interdisciplinary Program and Liquid Crystal Institute, Kent State University, Kent, OH 44242-0001, USA, Univ of Konstanz, Univ College London, NIST, Hiroshima Univ, KIT, Missouri University of Science and Technology, University of California, San Diego, Georgia Institute of Technology, KSU, SKKU, Lock Haven Univ, Massachusetts General Hospital, University of Science and Technology of China, Yale University, Shanghai Institute of Microsystem and Information Technology, CAS, Nanjing University, Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA, Department of Physics, Kent State University, Kent OH 44242, Department of Electro-Optic Engineering Ilse Katz Institute for Nanoscale Science and Technology Ben Gurion University, Beer Sheva 84105, Israel, Ohio University Zanesville

  • Frazier Baker

    Youngstown State University, Kent State University, Liquid Crystal Institute, Kent State University, Department of Biological Sciences, Kent State University, Department of Physics, Department of Chemistry and Biochemistry, Kent State University, Stony Brook Univ, Ohio Univ, Institute for Advanced Simulation, Institut fur Kernphysik, and Julich Center, Bowling Green State University, Dept. of Physics, Hiram College, Ohio State Univ - Columbus, Kent State University, Psychology Dept, Cleveland State University, Physics Dept, Cleveland State University, Chemical Physics Interdisciplinary Program and Liquid Crystal Institute, Kent State University, Kent, OH 44242-0001, USA, Univ of Konstanz, Univ College London, NIST, Hiroshima Univ, KIT, Missouri University of Science and Technology, University of California, San Diego, Georgia Institute of Technology, KSU, SKKU, Lock Haven Univ, Massachusetts General Hospital, University of Science and Technology of China, Yale University, Shanghai Institute of Microsystem and Information Technology, CAS, Nanjing University, Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA, Department of Physics, Kent State University, Kent OH 44242, Department of Electro-Optic Engineering Ilse Katz Institute for Nanoscale Science and Technology Ben Gurion University, Beer Sheva 84105, Israel, Ohio University Zanesville