Find the particular solutions of the following equations:
(1) x´´+ 6x´+13x = 13t +19 .
(2) x´´+ 6x´+13x = e−3t .
(3) x´´+ 6x´+13x = e−3t cos(2t) .
(1) Find the solution of x . Sketch some solutions.
(2) What is the largest growing rate g(x) that will allow for a constant quantity of
your vegetable?
(3) You can maintain the growing rate g(x) = 3 over a long period of time, with a
constant vegetable mass. What must that mass be, approximately?
Consider a parabola y = ax2 + bx + c passing though the points (x1, y1) = (−2,1.4) ,
(x2 , y2 ) = (0,−0.6) , and (x3 , y3 ) = (3,0.9) . The curve-fitting problem can be
modeled as a linear system:
Construct the system matrix A and solve for the parameters [a b c]T . Plot the
parabola and find the (x, y) coordinate of the minimum point.
The Fourier transform pair is given by
(1) Explain, in as much detail as you can without resorting to any physical examples,
the meaning of the expression for x(t) .
(2) Calculate, showing all the work, the Fourier transform of x(t) , where
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