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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.
how many words can be formed from letters of word daughter such that word contain 2vowles and 3consonant
base also called what
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Prove that the area of a rhombus on the hypotenuse of a right-angled triangle, with one of the angles as 60o, is equal to the sum of the areas of rhombuses with one of their angles
.755 convert to a percent
Twice a number increased by 11 is equal to 32 less than three times the number. Find out the number. Let x = the number. Now translate every part of the sentence. Twice a numb
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