A crucial step in measuring gravitational acceleration using a Kater pendulum is to equalize the periods of its normal and inverted oscillations. This paper takes the oscillating period difference of a Kater pendulum in its normal and inverted configurations as the objective function, and presents a monotonicity and sensitivity analysis of this function with respect to three configuration parameters: hanging point, large bob, and small bob positions. Based on this analysis, we propose an efficient algorithm for finding the configuration parameters with isochronous normal and inverted oscillations in Kater pendulum, significantly reducing the number of adjustments required and substantially improving experimental efficiency.