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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.
Speaking Mathematically : A Class 2 teacher was explaining the concept of place value to his students, using the number eleven. He started by saying "One and one make eleven." So
give an example of a relation R that is transitive while inverse of R is not
if oranges cost $2.40 a dozen, how much do 2 oranges cost?
Some Definitions of e 1. 2. e is the unique +ve number for which 3. The second one is the significant one for us since that limit is exactly the limit
A 64-ounce bottle of detergent costs $3.20. What is the cost per ounce of detergent? To ?nd out the cost per ounce, divide the cost through the number of ounces; $3.20 ÷ 64 =
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in one point of the circle only one tangent can be drawn. prove
Example of Cartesian coordinate Graph: Example: The temperature of water flowing in a high pressure line was measured at regular intervals. Plot the subsequent recorded da
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n(aubuc)..
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