Resumen de Rectangular Compound Pendulums
The compound pendulum1 provides an introduction to simple harmonic motion,2 measurement of moments of inertia,3 and large-amplitude motion to study nonlinear oscillations.4 A classic introductory experiment for investigating the properties of compound pendulums is the measurement of the periods of a set of rings of different diameters suspended at their circumferences,5–7 and the present experiment is a variation on this theme. A study of the periods of rectangular pendulums, suspended at the midpoints of their sides, as a function of the rectangle aspect ratio has been reported by Freeman.8 The measurement of the periods of square pendulums, suspended from their corners, as a function of the length of their sides has been suggested by Weltin5 as an inexpensive alternative to the use of rings. The present paper extends this experiment to encompass rectangles of different aspect ratios, from thin rectangles to squares, in order to demonstrate that when they are suspended from one corner, the period of oscillation only depends on the length l of the diagonal, and not on the aspect ratio. Although metal rectangles with pivots at one corner together with electronic timing could be used in the laboratory, the present experiment was intended as a take-home exercise and so used cardboard rectangles with a small-diameter pin at one corner, or one quarter along the diagonal, acting as the pivot and the use of a smartphone as a stopwatch.
