Bungee jump -> differential equation -> simulink simulation

In summary, a user on a forum found help with simulating a bungee jump model using Google. They have already done the simulation with zero initial values but want it to be more realistic. The user suggests that all forces should be acting together until there is a balance between them and provides the canonical form for the simulation. They also include a screenshot of their current model and ask for guidance on what to edit. Another issue they encountered was the velocity and acceleration going below zero at some point, but they were able to solve it using a switch. They also mention that their previous calculation for time, t(L) = sqrt(2*g*L), is incorrect as it does not account for air resistance. The user provides the values they used
  • #1
Wesker
4
0
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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  • #2
+ 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
 
  • #3
Ok I solved it with switch... and btw t(L) = sqrt(2*g*L) this is wrong as there is also air resistance..
 

Related to Bungee jump -> differential equation -> simulink simulation

1. What is a differential equation and how is it used in bungee jumping?

A differential equation is a mathematical equation that describes the relationship between a quantity and its rate of change. In bungee jumping, differential equations are used to model the motion of the jumper as they fall and are pulled back up by the bungee cord. This allows engineers to determine the ideal length and elasticity of the cord for a safe and thrilling jump.

2. How does a simulink simulation work in the context of bungee jumping?

Simulink is a software program that allows engineers to simulate and analyze complex systems. In the context of bungee jumping, simulink can be used to create a virtual model of the jumper and the bungee cord, allowing for accurate predictions of the jumper's motion and the tension in the cord during a jump. This can help engineers make adjustments to the design to ensure a safe and enjoyable experience for the jumper.

3. What factors are taken into account when creating a simulink simulation for bungee jumping?

When creating a simulink simulation for bungee jumping, engineers take into account various factors such as the weight and height of the jumper, the length and elasticity of the bungee cord, air resistance, and the force of gravity. These factors are used to create a realistic and accurate simulation of the bungee jump experience.

4. How do engineers ensure the safety of a bungee jump using differential equations and simulink simulation?

Engineers use differential equations and simulink simulation to calculate the tension and motion of the bungee cord during a jump. This allows them to determine the maximum safe height from which a person can jump, as well as the maximum weight that the cord can safely support. By taking into account these factors, engineers can ensure the safety of the bungee jump experience.

5. Can differential equations and simulink simulation be used for other extreme sports?

Yes, differential equations and simulink simulation can be used for various other extreme sports such as skydiving, base jumping, and zip lining. These mathematical tools allow engineers to accurately model and predict the motion and forces involved in these activities, ensuring the safety and enjoyment of participants.

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