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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.
a) A palindrome is a word that reads the similar whether read from right to left or from the left to right, the word ROTOR, for example. Let be the number of words of length n,
Rules of Integration 1. If 'k' is a constant then ∫Kdx = kx + c 2. In
Decision Trees And Sub Sequential Decisions A decision tree is a graphic diagram of different decision alternatives and the sequence of events like if they were branches of a t
who discovered unitary method
Explain Introduction to Non-Euclidean Geometry? Up to this point, the type of geometry we have been studying is known as Euclidean geometry. It is based on the studies of the a
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The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
-9+f ?-1 ?? (a-1)=-12 f(-3)=2
Q. Describe Laws of Cosines? The law of cosines is used to find the missing piece of a triangle if we are given either 1. Two sides and the included angle (SAS) or 2. All t
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