6.2Build code to satisfy, please. Objectives: Solve and understand dynamic systems equations sets like the Lorenz equations and the Rikitake model. Define and identify strange attractors and mathematical definition of chaos.Consider the Lorenz equations with initial conditions, x=y=z = 5 at t=0. Use a time increment from 0 to 20 with steps of 0.01.dxdtdydt= −ox + oy=rx-y-XZdzdtSet the constants = 10 and b=8/3.Part a) Assume r-10. You should find one stable point. Name your solution "XA","yA","ZA".Part b) Assume r-24.5. You should find one stable point and chaos co-exist. Name your solution "xB","yB","zB".Part c) Assume r=100. You should find a suprise. Name your solution "XC","yC","zC".Make sure you make the phase plots and time plots so you can identify each type of behavior.= -bz+xy

To solve the Lorenz equations and understand the dynamics of the system, we'll follow these…

Answered: Objectives: Solve and understand…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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3. Suppose the model of a vehicle suspension is given below. Write the equation of motion in matrix form (not in State Space form). Calculate the natural frequencies for k₁ k2 10 N/m, m2 = 50kg, and m₁ = 2000kg. -= - - 103 N/m, 1 x1(c) m1 www m1 Car mass k₁ Car spring k1 k₂ Tire stiffness www x2(1) m2 Tire mass м2 k₂ ↑
State the equation that mathematically represents the system. All in domain X(s) hint: there are 2 equations k₁ oooo m₁ B₁ X1 (1) B3 k₂ 0000 M2 B₂ x₂ (1) k3 0000
1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.
1 - Explain Van-Neumann stability by finite difference schemes for this equations a- Laplace equation. J²u dyz (x, y) = 0 J²u dx2(x, y) + b- poison equation. J²u J²u { (x, y) + əy² (x, y) = f (x, y) əx²
My question and answer is in the image. Can you please check my work? A 2 kg mass is attached to a spring with spring constant 50 N/m. The mass is driven by an external force equal tof(t) = 2 sin(5t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.)(a) Write the initial-value problem which describes the position of the mass. 2y"+50y=2cos(5t) (b) Find the solution to your initial-value problem from part (a). (1+(1/2)tcos(t))cos(5t)-(1/2)tcos(t) (c) Circle the letter of the graph below that could correspond to the solution. B (d) What is the name for the phenomena this system displays? Resonance
6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
The state X(t) of a dynamical system is solution of equation 10x (t) + 30ax(t) = 40, with a = 13. Calculate the rise time of the response.
Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
A mass of 2 kilograms is on a spring with spring constant k newtons per meter with no damping. Suppose the system is at rest and at time t = 0 the mass is kicked and starts traveling at 2 meters per second. How large does k have to be to so that the mass does not go further than 3 meters from the rest position? use 2nd order differential equations to solve (mechanical vibrations)
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xa 0- 1 point) Which of the systems presented on Fig. 2 is stable and which unstable? (a) t Fig. 2. System response (b) A
Equation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t). %3D a. Find the linearized equation of motion of the system for the motion that it makes around steady state equilibrium point x, under the effect of constant F, force. b. Find the natural frequency and damping ratio of the linearized system. - c. Find the step response of the system ( Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05m

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