In this paper, a novel method is proposed to avoid singularity and converge to the origin rather than the neighborhood in the terminal sliding mode control of second-order systems. Specifically, the proposed approach employs a power function whose exponent is state-dependent. The reason is that the limit of the derivative of this power function exists at the origin, effectively avoiding the common singularity issue in terminal sliding mode control. Moreover, this method ensures that both the convergence range and convergence time remain unaffected. However, it also introduces the challenge of increased chattering. Despite this drawback, the method is applicable to three different scenarios that require finite-time stability. Finally, the effectiveness of the proposed approach is validated through numerical simulations.