Applying the Dynamics of the Pendulum to the Design of a Playground Swing
World Transactions on Engineering and Technology Education
UNESCO * International Centre for Engineering Education
Place of Publication
In teaching mechanics courses, it is common practice to neglect nonlinear terms that arise in derivations. The reason used to justify this is that such approximations are adequate for small deformations. However, it is seldom clear how small is small or how large the maximum error is likely to be. The errors incurred by neglecting such terms are illustrated in this paper by taking the results of the dynamics of the pendulum and applying them to the design of a playground swing in a city park. The dynamic forces that arise during the operation of a swing are determined under the conditions of small angles and under those of large angles. The resulting forces are compared to see the effect of nonlinearity. Forces in the cables that support the seat of the swing are shown to be smaller when computed using the linearised equation of motion than those obtained from the nonlinear equation itself and the discrepancy between the two results increases with the magnitude of the initial angle that is given to the swing. The effect of this discrepancy on design is that the moments and forces used to design the beam and fasteners that hold the seat of the swing in place are underestimated significantly by linearising the driving force. The extent to which these forces are underestimated is quantified.
dynamics, pendulum, swing, playground, njock, libii
Josué Njock Libii (2007).
Applying the Dynamics of the Pendulum to the Design of a Playground Swing. World Transactions on Engineering and Technology Education.6 (2), 263-266. Australia: UNESCO * International Centre for Engineering Education.