Abstract: A general solution for the motion of single pendulum system and the equation for its eigenfrequency are given by solving the boundary value problem of equations for vibration of string, in which the tension is variation. The numerical solutions with high accuracy for the period of single pendulum system are obtained using the eigenfrequency equation. A fitting formula for the period of the system being in base-frequency vibration with high precision in the macro-range is found out.

Key words: single pendulum system, period, Bessel function, Neumann function