In this paper, we use the finite-difference time-domain (FDTD) method to simulate and study the electromagnetic response characteristics of ring and arc-shaped resonators. Firstly, we study the terahertz transmission properties of two single-ring resonators with different radii. Either the single-ring resonator with a large radius or with a small radius only has one resonance in the transmission spectra. Then, we combine those resonators into a double-ring resonator structure. The results conclude that the two resonant frequencies of the double-ring resonator are caused by the simple superposition of the resonances of the large and small radius single-ring resonators, respectively. Additionally, on the basis of a single-ring resonator, we also study the influence of the symmetrical and asymmetric arc-shaped resonators on electromagnetic response characteristics. The ring resonator is split from the middle into two symmetrical arc-shaped resonators. As the width of the middle gap gradually increases, the resonant frequency shows blueshift and the intensity of the surface current distribution gradually weakens. Finally, the direction of the current is reversed. In order to further compare the relationship between the single-ring resonators and the double-ring resonators, we study the double arc-shaped resonators. The main purpose of this paper is to study the frequency response characteristics of the ring resonator in the terahertz band and to control the terahertz spectrum by changing the symmetry of the ring resonator. In the future, we can further study the coupling response between the ring structures and the multi-frequency response modulation of the multi-ring structures.