This paper considers damped rotational oscillations about the vertical axis of a cylindrical permanent magnet that is horizontally suspended by a vertical inelastic thread. The damping of the oscillations is caused by eddy currents induced in aluminum foil that is placed horizontally below the magnet. A simplified mathematical model of the damped oscillations is proposed and verified by experiment qualitatively and quantitatively. It is shown that the relative energy loss during one oscillation depends linearly on the number of layers of aluminum foil and on the oscillation period. To measure the relative changes of the oscillation amplitude, a magnetic field sensor and data collection interface are used.

The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.

The Colorado School of Mines (CSM) has taught its first-semester calculus-based introductory physics course (Physics I) using a hybrid lecture/Studio Physics format since the spring of 1997. Starting in the fall of 2007, we have been converting the second semester of our calculus-based introductory physics course (Physics II) to a hybrid lecture/Studio Physics format, beginning from a traditional lecture/lab/recitation course. In this paper, we document the stages of this transformation, highlighting what has worked and what has not, and the challenges and benefits associated with the switch to Studio Physics. A major goal in this study is to develop a method for secondary implementations of Studio physics that keeps the time and resource investments manageable. We describe the history of Studio at CSM and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), exam scores, failure rates, and a variety of qualitative observations. Results suggest that Studio has increased student performance and satisfaction despite an aggressive expansion of class sizes in the past few years. Gains have been concentrated mostly in problem-solving skills and exam performance (as opposed to conceptual survey gains), in contrast to what has sometimes been seen in other studies.