恒定质量损失变质量振子的解析与实验研究
Analytical and Experimental Study of a Variable-Mass Oscillator with Constant Mass Loss
查看机构详情
- Rochester Community and Technical College（罗切斯特社区技术学院）
- Universitat Politecnica de Valencia（瓦伦西亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。
浏览论文内容
中文总结 AI 辅助
本研究通过解析和实验方法，研究了恒定质量损失的变质量振子，利用贝塞尔函数获得解析解，并通过实验验证了理论预测的准确性。
中文摘要 AI 辅助
我们提出了一个具有恒定质量损失的变质量振子的解析与实验研究。从质量随时间线性减少的弹簧-质量系统的运动方程出发，以贝塞尔函数的形式获得了解析解。随后推导出简单的渐近表达式，为振荡幅度和频率的演变提供了明确的描述。分析扩展到包含粘性阻尼，从而得到一个适合与实验观测直接比较的模型。使用一个简单的实验室装置进行了振子加速度的实验测量，该装置由一个弹簧安装的容器组成，该容器以近似恒定的速率持续损失质量。理论预测在整个振荡持续时间内准确地再现了测量的动力学，并且从拟合中获得的质量损失率与独立测量结果吻合良好。这些结果提供了一个易于理解的变质量动力学示例，并说明了特殊函数方法如何在高等本科力学中产生可实验检验的预测。
英文摘要
We present an analytical and experimental study of a variable-mass oscillator with constant mass loss. Starting from the equation of motion of a spring-mass system whose mass decreases linearly with time, analytical solutions are obtained in terms of Bessel functions. Simple asymptotic expressions are then derived, providing explicit descriptions of the evolution of the oscillation amplitude and frequency. The analysis is extended to include viscous damping, leading to a model suitable for direct comparison with experimental observations. Experimental measurements of the oscillator acceleration were performed using a simple laboratory setup consisting of a spring-mounted container that continuously loses mass at an approximately constant rate. The theoretical predictions accurately reproduce the measured dynamics over the entire duration of the oscillation, and the massloss rates obtained from the fits are in good agreement with independent measurements. The results provide an accessible example of variable-mass dynamics and illustrate how special-function methods can yield experimentally testable predictions in advanced undergraduate mechanics.
