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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.
If sin? = 1/2 , show that 3cos?-4cos 3 ? = 0. Ans: Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.
length of subnormal to the curve y2=2x+1 at (4,3)
Subjective Probability Probability may be determined by a personal statement of how likely an outcome is in a single trial or repetition of the same experiment. Since sub
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?
Is the group of order 10 simple?
In this case we will require deriving a new formula for variation of parameters for systems. The derivation now will be much simpler than the when we first noticed variation of pa
RANDOM VARIABLE A variable which assumes different numerical values as a result of random experiments or random occurrences is known as a random variable. The rainfal
y"-3y''-4y=2sinx
Q) In 3D-geometry give + and - signs for x,y,z, in all eight octants Ans) There is no specific hard rule for numbering the octants. So, it makes no real sense to ask which octan
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