Book contents
- Frontmatter
- Contents
- Preface
- Chapter 1 INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1)
- Chapter 2 THE LAW OF FALLING BODIES (Program 2)
- Chapter 3 THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS
- Chapter 4 INERTIA
- Chapter 5 VECTORS
- Chapter 6 NEWTON'S LAWS AND EQUILIBRIUM
- Chapter 7 UNIVERSAL GRAVITATION AND CIRCULAR MOTION
- Chapter 8 FORCES
- Chapter 9 FORCES IN ACCELERATING REFERENCE FRAMES
- Chapter 10 ENERGY: CONSERVATION AND CONVERSION
- Chapter 11 THE CONSERVATION OF MOMENTUM
- Chapter 12 OSCILLATORY MOTION
- Chapter 13 ANGULAR MOMENTUM
- Chapter 14 ROTATIONAL DYNAMICS FOR RIGID BODIES
- Chapter 15 GYROSCOPES
- Chapter 16 KEPLER'S LAWS AND THE CONIC SECTIONS
- Chapter 17 SOLVING THE KEPLER PROBLEM
- Chapter 18 NAVIGATING IN SPACE
- Chapter 19 TEMPERATURE AND THE GAS LAWS
- Chapter 20 THE ENGINE OF NATURE
- Chapter 21 ENTROPY
- Chapter 22 THE QUEST FOR LOW TEMPERATURE
- Appendix A THE INTERNATIONAL SYSTEM OF UNITS
- Appendix B CONVERSION FACTORS
- Appendix C FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY
- Appendix D ASTRONOMICAL DATA
- Appendix E PHYSICAL CONSTANTS
- SELECTED BIBLIOGRAPHY
- Index
Chapter 12 - OSCILLATORY MOTION
Published online by Cambridge University Press: 05 August 2013
- Frontmatter
- Contents
- Preface
- Chapter 1 INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1)
- Chapter 2 THE LAW OF FALLING BODIES (Program 2)
- Chapter 3 THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS
- Chapter 4 INERTIA
- Chapter 5 VECTORS
- Chapter 6 NEWTON'S LAWS AND EQUILIBRIUM
- Chapter 7 UNIVERSAL GRAVITATION AND CIRCULAR MOTION
- Chapter 8 FORCES
- Chapter 9 FORCES IN ACCELERATING REFERENCE FRAMES
- Chapter 10 ENERGY: CONSERVATION AND CONVERSION
- Chapter 11 THE CONSERVATION OF MOMENTUM
- Chapter 12 OSCILLATORY MOTION
- Chapter 13 ANGULAR MOMENTUM
- Chapter 14 ROTATIONAL DYNAMICS FOR RIGID BODIES
- Chapter 15 GYROSCOPES
- Chapter 16 KEPLER'S LAWS AND THE CONIC SECTIONS
- Chapter 17 SOLVING THE KEPLER PROBLEM
- Chapter 18 NAVIGATING IN SPACE
- Chapter 19 TEMPERATURE AND THE GAS LAWS
- Chapter 20 THE ENGINE OF NATURE
- Chapter 21 ENTROPY
- Chapter 22 THE QUEST FOR LOW TEMPERATURE
- Appendix A THE INTERNATIONAL SYSTEM OF UNITS
- Appendix B CONVERSION FACTORS
- Appendix C FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY
- Appendix D ASTRONOMICAL DATA
- Appendix E PHYSICAL CONSTANTS
- SELECTED BIBLIOGRAPHY
- Index
Summary
Another question concerns the oscillations of pendulums, and it falls into two parts. One is whether all oscillations, large, medium, and small, are truly and precisely made in equal times. The other concerns the ratio of times for bodies hung from unequal threads; the times of their vibrations, I mean. … As to the prior question, whether the same pendulum makes all its oscillations – the largest, the average, and the smallest – in truly and exactly equal times, I submit myself to that which I once heard from our Academician [Galileo]. He demonstrated that the moveable which falls along chords subtended by every arc [of a given circle] necessarily passes over them all in equal times. …
As to the ratio of times of oscillations of bodies hanging from strings of different lengths, those times are as the square roots of the string lengths; or should we say that the lengths are as the doubled ratios, or squares, of the times.
Galileo Galilei, Two New Sciences (1638)FINDING A CLOCK THAT WOULDN'T GET SEASICK
Navigation has provided one of the most persistent motives for measuring time accurately. All navigators depend on continuous time information in order to find out where they are and to chart their course. But until about two centuries ago, no one was able to make a clock that could keep time accurately at sea.
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- The Mechanical UniverseMechanics and Heat, Advanced Edition, pp. 295 - 334Publisher: Cambridge University PressPrint publication year: 1986