论文标题
悬浮的旋转的振荡
Oscillations of a suspended slinky
论文作者
论文摘要
本文讨论了春季（Slinky）自身重量的振荡。引入并将其与连续的治疗进行了比较，并将一个离散的模型描述为$ n $ springs和$ n $ springs和$ n $ springs。一个有趣的结果是，Slinky的上部执行三角形振荡，而如果Slinky以“自然”的初始条件开头，则底部几乎进行谐波振荡，在该条件下，弹簧仅在重力下方的休息位置向下拉，然后释放。还表明，振荡的周期仅由$ t = \ sqrt {32 l/g} $给出，其中$ l $是Slinky在其自身重量下的长度，而$ g $的重力加速度独立于弹簧的其他属性。
This paper discusses the oscillations of a spring (slinky) under its own weight. A discrete model, describing the slinky by $N$ springs and $N$ masses, is introduced and compared to a continuous treatment. One interesting result is that the upper part of the slinky performs a triangular oscillation whereas the bottom part performs an almost harmonic oscillation if the slinky starts with "natural" initial conditions, where the spring is just pulled further down from its rest position under gravity and then released. It is also shown that the period of the oscillation is simply given by $T=\sqrt{32 L/g}$, where $L$ is the length of the slinky under its own weight and $g$ the acceleration of gravity independent of the other properties of the spring.
