A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation...A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.展开更多
基金Funded by the National Natural Science Foundation of China (No. 50375113).
文摘A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.
