Bungee jump -> differential equation -> simulink simulation

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SUMMARY

The discussion focuses on simulating a bungee jump model using differential equations and Simulink. The canonical form of the equation is y''(t) = g - B/m*y'(t) - k/m*y(t), where B represents air resistance, m is the jumper's weight, and k is the elasticity ratio. The user initially implemented a model with zero initial values but seeks to enhance realism by incorporating the effects of air resistance and adjusting the timing of force applications. The user resolved some issues with a switch mechanism but noted inaccuracies in the timing equation due to air resistance.

PREREQUISITES
  • Understanding of differential equations, specifically second-order equations.
  • Familiarity with Simulink for modeling dynamic systems.
  • Knowledge of physics concepts such as elasticity and air resistance.
  • Basic programming skills to implement switches in simulations.
NEXT STEPS
  • Research how to implement air resistance in differential equations for more accurate simulations.
  • Learn about the use of switches in Simulink to manage state changes in simulations.
  • Study the effects of varying elasticity ratios on bungee jump dynamics.
  • Explore advanced techniques for modeling time-dependent forces in Simulink.
USEFUL FOR

This discussion is beneficial for physics students, engineers, and simulation developers interested in modeling dynamic systems, particularly those focusing on bungee jumping and similar applications.

Wesker
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Hello guys, I found this forum using google because I need help with simulating bungee jump model.
I've already done that with zero initial values and it looks good but I want it more realistic :
Let's say L is the length of rope so elasticity force starts acting when y=L so logically time should be
t(L) = sqrt(2*g*L)
I think that if t >=t(L) all forces should be acting togheter until there is not balance between them..
Canonical form is : y''(t) = g - B/m*y'(t) - k/m*y(t)
B - air resistance
m - jumper weight
k - elasticity ratio
I'm including screenshot of model I simulated so far...
What am I supposed to edit ?
Thanks for you answers!
 

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+ I can't figure out why in some point velocity and acceleration goes below zero... If someone could explain me resp. guide me how to correct it I'd be really glad :)
Values I used :
B = 13.08
m = 80
k = 2.83
 
Ok I solved it with switch... and btw t(L) = sqrt(2*g*L) this is wrong as there is also air resistance..
 

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