I really need help solving this problem with a brief explanation so I understand the method. Below I will post the Eq(4
Posted: Tue Apr 26, 2022 7:43 pm
I really need help solving this problem with a brief explanation
so I understand the method. Below I will post the Eq(4.41,
4.43) as well as Fig.4.19.
In the problem of the damped driven pendulum Eq(4.41,4.43) in T-M, set c = 0.05 and w = 0.7 and solve the equation for t' between 0 and 207 at F = 0.65 and F = 0.75, with x(0) = 0.2 and y(0) = 0.36 as the choice of initial conditions. (As usual y = .c) Obtain first the curves for y versus t', similar to the left most panel of Fig. 4.19. There is no need to draw the middle panel of Fig.4.19. For these values of F find and plot the points {z(v to), y(vto)} where to 21/W 27/0.7 and v = 1,2...20. Note: Pay attention to the accuracy of the differential equation solver. Although it is not necessary for submission, you might enjoy going beyond v = 20, and seeing how these “Poincare dots” begin to fill up the 2-d plane.
ž= -x - sin x + F cos ot' (4.41)
dy dt' - cy – sin x + F cos z x - (4.43)
Phase space plot Poincaré section F-0.4 F-0.5 0 wwwww M mun F 0.6 0 0 F 0 MAMLA F-0.8 www. Anna F:0.9 06 F = 1.0 0 0 0 10 Time 20 - Angle * Angle * FIGURE 4-19 The damped and driven pendulum for various values of the driving force strength. The angular velocity versus time is shown on the left, and phase diagrams are in the center. Poincaré sections are shown on the right. Note that motion is chaotic for the driving force F values of 0.6, 0.7, and 1.0.
so I understand the method. Below I will post the Eq(4.41,
4.43) as well as Fig.4.19.
- I Really Need Help Solving This Problem With A Brief Explanation So I Understand The Method Below I Will Post The Eq 4 1 (60.33 KiB) Viewed 36 times
- I Really Need Help Solving This Problem With A Brief Explanation So I Understand The Method Below I Will Post The Eq 4 2 (4.04 KiB) Viewed 36 times
ž= -x - sin x + F cos ot' (4.41)
dy dt' - cy – sin x + F cos z x - (4.43)
Phase space plot Poincaré section F-0.4 F-0.5 0 wwwww M mun F 0.6 0 0 F 0 MAMLA F-0.8 www. Anna F:0.9 06 F = 1.0 0 0 0 10 Time 20 - Angle * Angle * FIGURE 4-19 The damped and driven pendulum for various values of the driving force strength. The angular velocity versus time is shown on the left, and phase diagrams are in the center. Poincaré sections are shown on the right. Note that motion is chaotic for the driving force F values of 0.6, 0.7, and 1.0.