In this work, planar free vibrations of a single physical pendulum are investigated both experimentally and numerically. The laboratory experiments are performed with pendula of different lengths, for a wide range of initial configurations, beyond the small angle regime. In order to approximate the air resistance, three models of damping are considered—involving the three components of the resistive force: linear (proportional to velocity), quadratic (velocity-squared) and acceleration-dependent (proportional to acceleration). A series of numerical experiments is discussed, in which the damping coefficients are estimated by means of several computational methods. Based on the observed efficiency, a gradient method for optimization is treated as the main tool for determination of a single set of damping parameters, independent of the system’s initial position. In the model of resistive force, the term proportional to acceleration, associated with the empirical Morison equation, seems to be indispensable for the successful approximation of the real pendulum motion.

中文翻译：

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摆平面运动中各种阻尼模型参数的估计

在这项工作中，通过实验和数值研究了单个物理摆的平面自由振动。实验室实验是用不同长度的钟摆进行的，对于各种初始配置，超出小角度范围。为了近似空气阻力，考虑了三种阻尼模型——涉及阻力的三个分量：线性（与速度成比例）、二次（速度平方）和加速度相关（与加速度成比例）。讨论了一系列数值实验，其中阻尼系数是通过几种计算方法来估计的。根据观察到的效率，将梯度优化方法作为确定单组阻尼参数的主要工具，独立于系统的初始位置。在阻力模型中，与经验的 Morison 方程相关的与加速度成正比的项似乎对于成功逼近真实的钟摆运动是必不可少的。