Write a code to investigate the type of the critical point for the given linear system and construct a phase portrait.

Question

Want to see the full answer?

Answer 1

Question

Chapter 6.2, Problem 21P

Program Plan Intro

Write a code to investigate the type of the critical point for the given linear system and construct a phase portrait.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

A damper (or dashpot) is connected to the mass M of the previous problem. This could represent air resistance. The entire system could be a simple model of an automobile wheel suspension system (assuming the automobile body immobile in a vertical direction). Then the damper acts as a shock absorber. As before, the system is displaced and released and x(tg) = x, and v(to) = vo - It can be shown that the motion of the system Is described by the following differential equation: Mx + Dx + Kx(t) = 0 where D is the damping factor of the dashpot and x = v(t) = velocity at time t. Model and simulate the motion of the system from timet= to to t= tf, using a digital computer program, FIG. 1 DAMPER 3 SPRING FIG.I M MASS

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…

2. Interatomic (in pair) forces (energies) wrt distances between. a) Write a prg to obtain the plot of the function of Morse Potential Eq, and then, on that experiment parameters (arguments), to determine the rages of the coefficients that make the function inexplicit and explicit (visible), and save your plots and with your scripts and comments and submit. b) The same for the Lennard-Jones potential Egns. Determine the range of the coefficients you are applying. You need to demonstrate here in three steps!!. Plotting each in parts and adding them up. And submit.