<p>Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting, actuation, bionic instrumentation, and autonomous robotics. However, it is challenging to obtain analytical solutions describing these systems, which hinders analysis and design. In this work, we propose a self-vibrating liquid crystal elastomer (LCE) fiber-spring system exposed to spatially-constant gradient light, and determine analytical solutions for its amplitude and period. First, using a dynamic model of LCE, we obtain the equations governing the self-vibration. Then, we analyze two different motion states and elucidate the mechanism of self-vibration. Subsequently, we derive analytical solutions for the amplitude and frequency using the multi-scale method, and compare the solutions with numerical results. The analytical outcomes are shown to be consistent with the numerical calculations, while taking far less computational time. Our findings reveal the utility of the multi-scale method in describing self-vibration, which may contribute to more efficient and accurate analyses of self-vibrating systems.</p>