Model Comparison in the Introductory Physics Laboratory

Model comparison is at the heart of all scientific methodologies. Progress is made in science by constructing many models (possibly of different complexities), testing them against measurements, and determining which of them explain the data the best. It is my observation, however, that in many introductory physics labs we provide students with the materials and methods to verify the “correct” model of the experiment they are performing, e.g. measuring “g” or verifying the period of a pendulum. In this way, we do our students a disservice and don’t allow them to experience the richness and creativity that constitutes the scientific enterprise. Limiting the lab to the “correct” model can have its uses—for example, getting the students to practice the proper methods to measure lengths and times or to support the specific theory covered in the lecture portion of the class. However, when students perform these labs, they come to view these activities as repetitive and mechanical, reinforcing the notion that science concerns not the true exploration of nature but simply the verification of what we already know. By verifying what we already know, the laboratory experience does not improve overall understanding and can mislead students about the methods of science overall

An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

The effect of colored noise on heteroclinic orbits

The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of the system, is derived analytically in the case where noise is an additive Kubo-Anderson process. This theory shows how the geometry of the separatrix, as well as the noise intensity and correlation time, affect the statistics of crossing. Results can be applied to a wide variety of systems, and are valid in the limit where the noise correlation time scale is much smaller than the time scale of the undisturbed Hamiltonian dynamics

Using humanoid robots to study human behavior

Our understanding of human behavior advances as our humanoid robotics work progresses-and vice versa. This team's work focuses on trajectory formation and planning, learning from demonstration, oculomotor control and interactive behaviors. They are programming robotic behavior based on how we humans “program” behavior in-or train-each other