Asymmetries on a three-coupled-oscillator system: Their use in a gravitational-radiation detector
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A system composed of three coupled oscillators having the same resonant frequency is analysed. This system, which is the representation of the real physical system composed of a resonant gravitational-wave antenna equipped with a capacitive transducer and connected to a superconducting current amplifier, presents a series of asymmetries in the normal modes. An analytical evaluation of the resonant frequencies of the three normal modes of this system is given. These three normal modes are not equivalent, and their behaviour is the object of the present paper. The quality factors of the normal modes are calculated, showing that the central-mode quality factor is very weakly affected by the lowest one of the three oscillators, namely the electricalQ. A second asymmetry is then found by calculating the spread of a pulse of energy deposited into the first oscillator: it is shown that most of this energy is detected in the central mode. These two asymmetries permit to increase the sensitivity of the system calculated for the central mode. A third asymmetry is then analysed concerning the different contribution of each oscillator to the thermal noise of each mode. Supposing, as it is in the real case, that the three oscillators are in equilibrium, but at different thermodynamic temperatures, an equivalent thermodynamic temperature is calculated for each mode. This last feature can then be used to lower the equivalent temperature of the central mode without the need of cooling all the three oscillators at the same low temperature.
KeywordsQuality Factor Normal Mode Lateral Mode Couple Oscillator Central Mode
- PACS 04.80
Experimental tests of general relativity and observations of gravitational radiation
- PACS 03.20
Classical mechanics of discrete systems: general mathematical aspects
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- W. O. Hamilton andW. M. Fairbank:VI International Conference on General Relativity and Gravitation, (Copenhagen, 1971).Google Scholar
- H. J. Paik:Rev. Sci. Instrum.,47, 1168 (1976).Google Scholar
- J. P. Richard:Proceedings of the II Marcel Grossmann Meeting, Trieste, Italy, July 1979.Google Scholar
- M. G. Castellano andC. Cosmelli:Nuovo Cimento C,7, 9 (1984).Google Scholar
- H. F. Olson:Dynamical Analogies, (Van Nostrand, Princeton, N. J., 1958).Google Scholar
- The main point of this paragraph has been presented by the author at the IX Convegno di Relatività Generale e Fisica della Gravitazione, Capri, Italy, September (1990).Google Scholar