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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 group of ?ve friends gone out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the similar, so they needed to split the bill evenly. Without consider
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Evaluate following limits. (a) (b) Solution There in fact isn't a whole lot to this limit. In this case because there is only a 6 in the denominator we'l
The probability that a person will get an electric contract is 2/5 and the contract that he will not get plumbing contract is 4/7.If the probability of getting at least one contra
x>4
DEVELOPING PRE-NUMBER CONCEPTS : Previously you have read how children acquire concepts. You know that, for children to grasp a concept, they must be given several opportunities
what is 5x - 14x + 7x =
What is Inductive Reasoning ? Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the
which ratio is largar. 1. 15:16 or 24:25
A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth. a. 34.5 cm b. 32.1 cm c. 35.2 cm d. 33.3 cm
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