Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integrals, which cannot be expressed in terms of elementary functions, and therefore a wide variety of approximations have been published. These range from simple single-term formulae to more sophisticated equations, which apply to a wider range of amplitudes, to an iterative procedure for calculating the precise period. The published approximations are compared as Taylor series expansions, and graphically to indicate their accuracy and their regions of applicability.

现在可以使用包括MEMs陀螺仪/加速度计在内的多种仪器来进行摆幅作为振幅函数的精确测量，因此需要理论表达式进行比较。不幸的是，摆方程的精确解涉及椭圆积分，而椭圆积分不能用基本函数表示，因此已经发表了各种各样的近似值。这些范围从简单的单项公式到适用于更大幅度范围的更复杂的方程式，再到用于计算精确周期的迭代程序。将已发布的近似值作为泰勒级数展开进行比较，并以图形方式表示其准确性和适用范围。