According to the graph comparing the maximum vertical displacements of various bungy cords,
Cord 7 (with a cord length of 21 meters and a spring constant of 50) and Cord 8 (with a cord
length of 21 meters and a spring constant of 60) are the most effective that performs the
alternatives to a great extent. It offers the most vertical displacement and breaks through the
fully dunked threshold. Implying that it facilitates the most thrilling bungy jump possible for the
jumper.
By looking at the charts, we can get an idea of when and at which velocity the jumper hits the water. Approximately 2 seconds after jumping, the jumper appears to hit the water at a speed of 18 m/s.
The jumper's maximum vertical displacement will be reduced as a result of the additional mass. In order to accommodate the additional weight, the bungy cord will need to stretch even further. As a result, the jumper will be able to reach the water's surface faster, have a slower impact velocity, and take longer to do so.
The Lorenz system never reaches a stable state and is chaotic by definition. Instead, it demonstrates an unusual attractor—a complex, non-repeating behavior. The system's chaotic and irregular oscillations, in which it continuously explores new states and does not converge to a single point, are depicted by the phase plot (Lorenz butterfly) and the timeseries plot. In conclusion, the Lorenz system is a typical illustration of a chaotic system that exhibits sensitivity to initial conditions and lacks a steady-state or long-term equilibrium.
When you use a second set of initial conditions (x (0) = y (0) = z (0) = 1.001) in Step 6 to solve the Lorenz system, you will notice that the solution differs from the original. The first set of initial conditions (x (0) = y (0) = z (0) = 1.0) led to the solution over time. Chaotic systems' extreme sensitivity is demonstrated by this behavior. To beginning conditions, like the Lorenz framework. It is essential to keep in mind, in terms of numerical accuracy, that chaotic systems are fundamentally unpredictable in the long run due to their sensitivity to initial conditions. Long-term outcomes could be vastly different from one another even with relatively minor variations in starting conditions. In a chaotic system, predicting the precise values of x, y, and z at any given time is extremely challenging due to this sensitivity. numerical errors in chaotic systems can aggregate and intensify over the long term, making long-term gauges really sketchy. Therefore, it is frequently impossible to accurately predict the precise values of the variables in chaotic systems. Instead, the qualitative behavior of attractors like the Lorenz attractor and statistical characteristics of chaotic systems are frequently the focus of research.