Damped simple harmonic motion of a modified physical pendulum

Abstract A physical pendulum of mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> was modified in the form of a cone made from folder cardboard to introduce non-negligible damping. The mass of the physical pendulum and the area of the cone base were varied. A satisfactory match between the theoretical model and experimental data was obtained; the damping constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> was obtained in both variations. The damping constant exhibited a positive linear relationship with area, and an inversely proportional relationship with mass. This experiment provided an easy means for students to verify the relationships with the damping constant and with both mass and area.