模拟一个下降的slinky
Modeling a falling slinky
摘要：
弹簧是拉伸弹簧的一个例子：在未拉伸的状态下，弹簧是折叠的，匝接触，并且需要有限的张力来将匝从这种状态中分离出来。如果一个紧身衣从它的顶部悬挂下来，在重力的作用下伸展，然后释放，紧身衣的底部不会开始下降，直到紧身衣的顶部部分，从顶部依次倒塌，与底部碰撞。总塌陷时间t_c（对于真实的弹簧圈，通常约为0.3 s）对应于波前沿着弹簧圈传播以传递顶端释放所需的时间。我们提出了一个修改现有的模型下降的张力弹簧（卡尔金1993年），并将其应用到数据从两个真正的slinkies电影下降。该模型的修改是包括一个有限的时间崩溃的曲折的苗条背后的崩溃前线传播下来的苗条在下降期间。新的有限崩溃时间模型实现了一个很好的定性拟合的实际slinkies在测量的下降过程中的顶部观察到的位置。每个弹簧的弹性常数k取为模型中的自由参数。每个弹簧的k的最佳拟合模型值与从弹簧的振荡的测量周期获得的值近似一致。
英文摘要：
A slinky is an example of a tension spring: in an unstretched state a slinky is collapsed, with turns touching, and a finite tension is required to separate the turns from this state. If a slinky is suspended from its top and stretched under gravity and then released, the bottom of the slinky does not begin to fall until the top section of the slinky, which collapses turn by turn from the top, collides with the bottom. The total collapse time t_c (typically ~0.3 s for real slinkies) corresponds to the time required for a wave front to propagate down the slinky to communicate the release of the top end. We present a modification to an existing model for a falling tension spring (Calkin 1993) and apply it to data from filmed drops of two real slinkies. The modification of the model is the inclusion of a finite time for collapse of the turns of the slinky behind the collapse front propagating down the slinky during the fall. The new finite-collapse time model achieves a good qualitative fit to the observed positions of the top of the real slinkies during the measured drops. The spring constant k for each slinky is taken to be a free parameter in the model. The best-fit model values for k for each slinky are approximately consistent with values obtained from measured periods of oscillation of the slinkies.
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