Book contents
- Frontmatter
- Contents
- Preface to Part 1
- Preface to Part 2
- Preface to the combined volume
- 1 General introduction – author to reader
- PART 1 THE SIMPLE CLASSICAL VIBRATOR
- 2 The free vibrator
- 3 Applications of complex variables to linear systems
- 4 Fourier series and integral
- 5 Spectrum analysis
- 6 The driven harmonic vibrator
- 7 Waves and resonators
- 8 Velocity-dependent forces
- 9 The driven anharmonic vibrator; subharmonics; stability
- 10 Parametric excitation
- 11 Maintained oscillators
- 12 Coupled vibrators
- PART 2 THE SIMPLE VIBRATOR IN QUANTUM MECHANICS
- Epilogue
- References
- Index
11 - Maintained oscillators
Published online by Cambridge University Press: 13 January 2010
- Frontmatter
- Contents
- Preface to Part 1
- Preface to Part 2
- Preface to the combined volume
- 1 General introduction – author to reader
- PART 1 THE SIMPLE CLASSICAL VIBRATOR
- 2 The free vibrator
- 3 Applications of complex variables to linear systems
- 4 Fourier series and integral
- 5 Spectrum analysis
- 6 The driven harmonic vibrator
- 7 Waves and resonators
- 8 Velocity-dependent forces
- 9 The driven anharmonic vibrator; subharmonics; stability
- 10 Parametric excitation
- 11 Maintained oscillators
- 12 Coupled vibrators
- PART 2 THE SIMPLE VIBRATOR IN QUANTUM MECHANICS
- Epilogue
- References
- Index
Summary
This chapter is concerned only with simple systems in steady oscillation, such as were classified in chapter 2 under the heading of negative resistance devices, feedback oscillators and relaxation oscillators. Here we shall attempt to refine the description and classification of the different types though, as is common in such attempts, firm divisions are hard to find. At the same time we shall analyse a number of examples so as to understand what conditions must be satisfied for them to oscillate spontaneously, how the amplitude of oscillation is limited by non-linearity, and what determines the ultimate waveform. No attempt will be made to establish rigorously the general conditions for oscillation to occur. This is an important and well-studied problem, but one which deserves the fuller treatment that will be found in specialized texts.
It has already been remarked, in chapter 2 and elsewhere, that a resonant system governed by a second-order equation such as (2.23) will oscillate spontaneously if k is negative. A source of energy is required to overcome inevitable dissipative effects, and among the many examples of how the energy may be injected probably the commonest is by feedback. Let us start, then, with a general survey of the feedback principle, with particular reference to the influence feedback may have on the performance of a resonant system, and not solely in setting it in spontaneous oscillation. The argument will be conducted in terms of electrical circuits, which account for the overwhelming majority of applications.
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- The Physics of Vibration , pp. 306 - 364Publisher: Cambridge University PressPrint publication year: 1989