A simple numerical method is used to calculate the velocity and displacement from the acceleration at successive time steps given a set of initial conditions. The method outlined is not the most accurate method but one in which is easy to implement. If the values of x(t), and are known at time then the values at time + are y(t), vx(t), vy(t), ax(t) ay(t) t t t (6a) (6b) Once the acceleration, velocity and displacement are known, it is a simple matter to calculate forces and energies. The kinetic energy of the jumper the elastic potential EK, energy the gravitational potential energy and the total mechanical energy are EP, EG E given in equation (7). The zero for the gravitational potential energy is chosen to be at = 0. y (7a) (7b) (7c) (7d) Table 1 summarize the input parameters and possible range of values for running the mscript osc_bungee.m. Table 1: Jump parameters: Parameters are changed within the mscript. Variable Symbol Value Unit mass of jumper 50 to 150 kg m natural length of bungee cord 6 to 20 m L stiffness of bungee cord: ~ 250 N.m-1 k1 stiff cord ~ 150 k2 stiffness of bungee cord: ~ 200 N.m-1 k1 medium cord ~ 110 k2 stiffness of bungee cord: ~ 160 N.m-1 k1 soft cord ~ 80 k2 extension for change in stiffness of 4 to 6 m e1 bungee cord max tensile strength of bungee cord ~ 2.0104 N Smax elongation factor 2 to 4 e / L
A simple numerical method is used to calculate the velocity and displacement from the acceleration at successive time steps given a set of initial conditions. The method outlined is not the most accurate method but one in which is easy to implement. If the values of x(t), y(t), vx(t), vy(t), ax(t) and ay(t) are known at time t then the values at time t + t are (6a) (6b) Once the acceleration, velocity and displacement are known, it is a simple matter to calculate forces and energies. The kinetic energy of the jumper EK, the elastic potential energy EP, the gravitational potential energy EG and the total mechanical energy E are given in equation (7). The zero for the gravitational potential energy is chosen to be at y = 0. (7a) (7b) (7c) (7d) Table 1 summarize the input parameters and possible range of values for running the mscript osc_bungee.m. Table 1: Jump parameters: Parameters are changed within the mscript. Variable Symbol Value Unit mass of jumper m 50 to 150 kg natural length of bungee cord L 6 to 20 m stiffness of bungee cord: stiff cord k1 k2 ~ 250 ~ 150 N.m-1 stiffness of bungee cord: medium cord k1 k2 ~ 200 ~ 110 N.m-1 stiffness of bungee cord: soft cord k1 k2 ~ 160 ~ 80 N.m-1 extension for change in stiffness of bungee cord e1 4 to 6 m max tensile strength of bungee cord Smax ~ 2.0104 N elongation factor e / L 2 to 4
osc_bungee.docx