This paper investigates the work and energy changes in the forced vibration of a pendulum, deriving the work done by damping torque, elastic torque, and driving torque within a quarter cycle, as well as their resonance equilibrium conditions. Subsequently, from an energy perspective, the relationship between the average values of the pendulum's kinetic and potential energy and the vibration frequency is studied. Finally, the instantaneous power of the damping torque and driving torque is analyzed, and the trend of the pendulum's amplitude change is explained from the perspective of amplitude decay. This paper provides a theoretical reference for analyzing the work done by torques and the energy transformation during the forced vibration process.

Refractive index is not only related to geometric optics, but also closely related to wave optics, and its measurement methods are varied. In order to study the influence of different methods on the accuracy of refractive index measurement, the refractive index of a prism is measured by three different experimental methods, including grazing method, minimum deviation angle method and Brewster angle method. The refractive index was analyzed and compared. The experimental results show that compared with Brewster angle method, the grazing method and minimum deviation angle method are more accurate in measuring the refractive index.This paper provides an experimental method for accurate measurement of refractive index of prism.