The spring-mass system studied in undergraduate physics laboratories may exhibit complex dynamics due to the simultaneous action of gravitational and elastic forces in addition to air friction. In the first part of this paper, we describe a laboratory experiment aimed at beginner students which also gives those with a more advanced background an opportunity to explore more complex aspects of the motions involved. If students are not given predefined apparatus but are allowed instead to design their own set-up for the experiment, they may also learn something about the thought processes and experimental procedures used in physics. In the second part of this paper, we present a systematic study of the parametric behavior of the system because teachers have to master its dynamics. The non-linear interaction between the vertical and the pendular oscillations in a vertical spring-mass system depends on the ratio between the frequencies of the two motions and on the motion's excitation. Systematic experimental investigations, coupled with relevant simulations, highlight the many aspects of physics involved in the partition of energy transfer between the two modes. The different motion waveforms obtained by sweeping through the resonance curve and by applying small and strong excitations are presented and analyzed. The influence of the unavoidable spurious motions is investigated. An analogy between the parametric interaction in a spring--mass system and that found during frequency conversion in non-linear optical crystals is discussed.
A Framework for Understanding the Impact of Integrating Conceptual and Quantitative Reasoning in a Quantum Optics Tutorial on Students' Conceptual Understanding
University of Cincinnati（辛辛那提大学）；Community College of Allegheny County（阿勒格尼县社区学院）；University of Pittsburgh（匹兹堡大学）
Interactive and accessible quantum key distribution modules for introducing students to quantum science and engineering
Institute for Quantum Computing (IQC) University of Waterloo（量子计算研究所，滑铁卢大学）；Pearl Sullivan Engineering IDEAs Clinic, Faculty of Engineering University of Waterloo（珍珠沙利文工程IDEAS诊所，工程学院，滑铁卢大学）
