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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) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by
Write down the system of differential equations for mass system and the spring above. Solution To assist us out let's first take a rapid look at a situation wherein both of
In the introduction of this section we briefly talked how a system of differential equations can occur from a population problem wherein we remain track of the population of both t
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advanteges of duality
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A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 liter of 82 proof bourbo
Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage. Ans: A tree is a graph like t
TYPES OF COMPUTERISED PAYROLL PACKAGES
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
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