Although many methods for solving the problem of the vibration of collision have been derived, Suzuki's theory based on the superposition theory and mechanical indicial admittance makes it easy to seize physical meanings, because its correspondence with the electrical circuit is clear. Suzuki has treated the case in which a moving body collide with a stationary one, and has only discussed the phenomena during collision. Here in this paper, the authors complement and generalize Suzuki's theory. In the case in which two moving bodies collide with each other, two equations can be applied to the phenomena before, during, and after the collision concerning each body respectivery. Also this method is made applicable not only to elastic collision, but also to impulsive collision. This fundamental equation is analogous to that of Newton's impact theory. Finally, equivalent circuits of colliding systems are derived from the fundamental equation.
An exact analytical expression in compact form is obtained for the intensity distribution of the diffraction spectra produced by sawtooth ultrasonic waves. The intensity of the s-th order diffraction spectrum is expressed as Is=[v/(v-sk)J_s(v-sk)]^2, s=0, ±1, ±2, . . . . . where v is the phase-lattice parameter (amplitude of phase modulation of the light wavefront produced by crossing the ultrasonic beam), and k is the sawtooth parameter. J_s is the Bessel function of the s-th order, and the sign of s is positive for the diffraction spectra with positive components of the propagation vector in the direction of propagation of ultrasound. General aspects of the diffraction spectrum of light produced by sawtooth waves are discussed.
General aspects of the diffraction spectrum of light produced by sawtooth ultrasonic waves as predicted by the theory are compared with those experimentally found, and good agreements are obtained. Methods are described for obtaining the nonlinearity parameter B/A of liquids from the diffraction spectra, and the nonlinearity parameter of water is obtained by this method (B/A=6. 5)