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Numerical Solution for Bungee Jump Problem

Numerical Solution for Bungee Jump Problem. 2009020076 박문규 2011018753 박준연 2011020404 박현수. contents. - Bungee Jump Equation - Matlab Code - Improved Euler’s methods - Runge-Kutta methods Numerical Result - Improved Euler’s methods - Runge-Kutta method

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Numerical Solution for Bungee Jump Problem

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  1. Numerical Solution for Bungee Jump Problem 2009020076 박문규 2011018753 박준연 2011020404 박현수

  2. contents • - Bungee Jump Equation • - Matlab Code • - Improved Euler’s methods • - Runge-Kutta methods • Numerical Result • - Improved Euler’s methods • - Runge-Kutta method • More... Mathematical modeling

  3. Bungee jump equation , Mathematical modeling

  4. Analytical approach Set Then = dt = v(t) = x(t) = Mathematical modeling

  5. NUMERICAL APPROACH 1. Improved Euler’s method , = 0 + = =v(2) = =

  6. NUMERICAL APPROACH 2. Runge - Kutta method = =

  7. Matlab code Improved Euler’s methods Mathematical modeling

  8. Matlab code Runge - Kutta methods Mathematical modeling

  9. Result Mathematical modeling

  10. Result Mathematical modeling

  11. more.. • We want to model the vertical dynamics of a jumper connected to a stationary platform with a bungee cord. F=ma • Forces: • mg (gravity, g = acceleration due to gravity) • cd v2(drag force, cd = drag coefficient, v = velocity) (need to always retard v, so if falling (v>0) need force neg, if rising (v<0) need force pos to reduce dv/dt) (use sign(v) for drag force) • k (x-L) (spring force, x = distance measured down from platform, L = rest length of cord) • γ v (damping force, γ is damping coefficient of cord) Mathematical modeling

  12. More... k =  = 0 if x  L If weight rises, then the force which defy free fall will decrease. Thus, both x(t) and v(t) increase faster. Mathematical modeling

  13. Thank you Mathematical modeling

  14. *Matlab code Mathematical modeling

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