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Consider the Van der Pol oscillator
x′′- µ(1 - x2)x′ + x = 0
(a) Write this equation as a system of first order equations
(b) Taking µ = 2, use MatLab's routine ode45 to compute the solution for the initial value problem x(0) = 0 and x′ (0) = 5 from t = 0 to t = 40. Plot x as a function of t and also plot x vs x′ in phase-space.
(c) Repeat for the initial conditions x(0) = 0 and x′ (0) = 0.01.
(d) What is the ?xed point of the system? Use your numerical results to argue what the long time behavior of the system is.
In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other app
For each of these arguments determine whether the argument is correct or incorrect and explain why. a) Everyone enrolled in the university has lived in a dormitory. Mia has never l
Illustration 2 In a described farm located in the UK the average salary of the employees is £ 3500 along with a standard deviation of £150 The similar firm has a local
Write the quadratic equation whose roots are real and non conjugate Ans) x^2-x+6=0 ...roots are real and non conjugate
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what is the meaning of statistics
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
Recognizes the absolute extrema & relative extrema for the given function. f ( x ) = x 2 on [-2, 2] Solution Following is the graph for this fun
Describe Common Phrases to Represent Math Operations? The table below shows the common phrases used in word problems to represent addition, subtraction, multiplication, and div
Total Contribution per Year for next 10yeras =$1000+$800 =$1800 So Total Future fund Vaule =$1800*(1+1.073+power(1.073,2)+ power(1.073,2)+ power(1.073,3)+ power(1.073,4)+ power
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