MAT 375 Module Three Guided Activity: Discrete Dynamical Systems Part 2 (Independent Practice) Help Please !!! I am in desperate need of help !!! Complete Problem 11 from Section 4.4. Your solution should be similar in scope to the example above, taking care to account for all steps in the five-step model. 11. Reconsider the docking problem of Example 4.3, and now assume that c = 5 sec, w = 10 sec, and k = 0.02. (a) Assuming an initial closing velocity of 50 m/sec, calculate the sequence of velocity observations v0, v1, v2, ... , predicted by the model. Is the docking procedure successful? (b) An easier way to compute the solution in part (a) is to use the iteration function G (x) = x + F (x), with the property that x (n + 1) = G (x (n) ). Compute the iteration function for this problem, and use it to repeat the calculation in part (a). (c) Calculate the solution x (l), x (2) , x (3), ... , starting at x (0) = (1, 0). Repeat, starting at x (O) = (0, 1). What happens as n ? What does this imply about the stability of the equilibrium (0, 0)? [Hint: Every possible initial condition x (0) = (a , b) can be written as a linear combination of the vectors (1, 0) and (0, 1), and G (x) is a linear function of x .] (d) Are there any states x for which G (x) = AX for some real A? If so, what happens to the system if we start with this initial condition? Part 3 (Analysis) These types of problems are very sensitive to initial conditions. Test different initial conditions to see if you can find parameters in which the technique would fail. SNHU MAT 375 Page 1 of 2 Module Three Guided Activity SNHU MAT 375 Page 2 of 2 Module Three Guided Activity PRINTED BY: Rebecca Hodges . Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. PRINTED BY: Rebecca Hodges . Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. PRINTED BY: Rebecca Hodges . Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. PRINTED BY: Rebecca Hodges . Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted