Solving a backpack vibration system using fourth-order runge-kutta methods

Abstract

A backpack vibration system involving ordinary differential equations has been developed in this study. The purpose of this research is to solve a biomechanical model of a backpack vibration system numerically. The model is a backpack-human trunk system, represented by a mass-spring system that uses a Fourier series as an external force to describe a motion of the backpack. The displacement and velocity of the backpack vibration system are determined using two numerical methods; the classical fourth-order Runge-Kutta method (RK4) and a modified fourth-order Runge-Kutta method, namely Arithmetic Mean fourth-order Runge-Kutta methods (AM-RK4). The numerical results obtained from these two methods are compared using the absolute errors. The result shows that RK4 gives better agreement and accuracy with the exact solution when compared to AM-RK4.