Search results

  1. L

    Identifying type of feedback by looking at bode plot

    Homework Statement Below is the bode plot of return difference, 1+C(S)P(S) in a feedback system. Identify the frequencies where the feedback is large, negative, positive and negligible. P(S) = \frac{100}{s^2+2s+1} C(S) = \frac{220(s+50)}{s+200} Homework Equations Bode Plot, Feedback The...
  2. L

    Finding the state space model of a nonlinear system

    So the evaluation at (-15,5) becomes y'= \begin{pmatrix} 0 & 20 \\ -1 & -3 \end{pmatrix} ?
  3. L

    Finding the state space model of a nonlinear system

    Homework Statement The state space model of a nonlinear system is x'_1(t) = 2x^2_2(t) - 50 x'_2(t) = -x_1(t) - 3x_2(t) + u(t) Where x_1(t) and x_2(t) are the states, and u(t) is the input. The output of the system is x_2(t). Find the state space model of this system linearized at the...
  4. L

    Drawing with trigonometric function

    Yeah, translating the axes by defining a new set of axes such as x' and y', then rotating it via trigonometric function but I was struggling big time about that. Any suggestions?
  5. L

    Drawing with trigonometric function

    No it can be in terms of X too. How should I modelize the lines which goes at 45 degree angle?
  6. L

    Drawing with trigonometric function

    Homework Statement Come up with a set of equations to draw the following picture: http://img197.imageshack.us/img197/7428/equation.jpg [Broken] Homework Equations The Attempt at a Solution The circle is easy. 1000 = sqrt(x^2+y^2) I can just model the equation with sines. So y_1 = 300...
  7. L

    Cumulative Distribution Function problem

    Oh.. Ok I'm still a bit lost on how to tackle this problem..:confused:
  8. L

    Cumulative Distribution Function problem

    Homework Statement Let the independent random variables X1,X2,X3 have the same cdf F(x). Let Y be the middle value of X1,X2,X3. Determine the cdf of Y. Homework Equations F(x) = P(X<=x) = ∫-inf to x f(y)dy The Attempt at a Solution I don't understand the question, what does it...
  9. L

    Discrete Probability Mass Function

    Twenty million dollars, ten million dollars and zero dollars?? (edit)nvm I figured out ty
  10. L

    Discrete Probability Mass Function

    Homework Statement A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal...
  11. L

    Random Grammar Question

    I know this probably isn't the best place to ask this question but here goes anyways lol What's wrong with the next sentence/ "What do you feel when you see a smoke detector? Do you ever feel like an astronaut? No? Well, the next time you see one, try to imagine that it's part of your...
  12. L

    Induction proof on list

    The class is known as Advanced Discrete Structures, crosslisted with Mathematics and Computer Science. Apparently we cover topics of both formal logic and abstract computer science. This is the notes we got from the professor. Maybe this would be of help...
  13. L

    Induction proof on list

    Did I finally break the experts here with an unsolvable question? Bump
  14. L

    Induction proof on list

    Homework Statement Prove by finite list induction ∀xs:: [a]. map (\x -> x) xs = xs Homework Equations map f [ ] = [ ] map f (x : xs) = (f x) : map f xs The Attempt at a Solution The list induction principle to prove a finite lists of type a is [P([ ])^ ∀x :: a. ∀xs ...
  15. L

    Really Simple Logarithmic Question

    Homework Statement 1. f(n) = log(n) ^ (log(n)). Simplify for Big-O notation. The Attempt at a Solution 1. I'm just trying to prove a big-O notation for one of my courses, and this was simplified to f(n) = n^log(log(n)) And I'm having a hard time seeing why. Any guidance would be...
  16. L

    Arithmetic Sequence Problem

    Uh so anyone got an idea about second problem?
  17. L

    Arithmetic Sequence Problem

    I understand how you simplified the equation.. but where did you get the idea of plugging 9,19,29 for n? nvm i see it now. TY.
  18. L

    Arithmetic Sequence Problem

    What.. is latex tag broken..?
  19. L

    Arithmetic Sequence Problem

    Homework Statement Problem 1: Two Arithmetic Sequences are given. a_n = 200,196,192,188,184.... [ltaex]b_n = 100,103,106,109,112....[/itex] For integers l,m, find the number of pairs consisting of (l,m) which satifies condition a_l = b_m Problem 2: Three terms, sin(x)...
  20. L

    Solving Quartic Equation using Derivative

    Homework Statement x^4 + 3x^3 - 7x^2 - 15x + 18 = 0 Find x Homework Equations First Derivative? Second Derivative? The Attempt at a Solution Normally, I'd use Ferrari's method to tackle this problem but I am required to use derivation to find the answer... Where do I go from here? Do...
  21. L

    Finding limit

    Homework Statement Find the limit of \frac{x^3-2x^2-9}{x^2-2x-3} as x->3 Homework Equations The Attempt at a Solution You factor the bottom portion and top portion, then it looks something like this \frac{x(x^2-2x)-9}{(x-3)(x+1)} I feel like I can go further about eliminating the...
  22. L

    Finding a volume bounded by a region

    Just so that I understand, why is it that the cylindrical shell method must be applied here? I was taught that when finding a volume revolved around X or Y axis, the above equation works well except you just have to be careful when you plug in for X or Y.
  23. L

    Finding a volume bounded by a region

    Homework Statement The region bounded by y=e^-x^2, y=0, x=0 and x=1 is revolved around the y-axis. Find the volume. Homework Equations V = \int_{a}^{b} R^2 dy The Attempt at a Solution We must first express x in terms of y. So we get \ln y = -x^2 x^2 = -\ln y We substitute this to the...
  24. L

    Upper bound and lower bound

    Homework Statement 1. f(n) = n - 100 g(n) = n - 200 2. f(n) = log(2n) g(n) = log(3n) n >= 0 in all cases Find out if f(n) is an upperbound, lowerbound or both of g(n) Homework Equations The Attempt at a Solution in case of 1, f(n) has to be an upperbound of g(n) because...
  25. L

    Arc Tangent Squared

    so [arctan(3)]^2 = arctan(3) * arctan(3) ?
  26. L

    Arc Tangent Squared

    Homework Statement tan(2x) - 3 cot (2x) = 0 Homework Equations Trigonometry Knowledge. The Attempt at a Solution tan(2x) - 3cot(2x) = 0 tan(2x) - 3/tan(2x) = 0 [tan(2x)]^2 - 3 = 0 [tan(2x)]^2 = 3 Is there such thing as Arc Tangent thats squared??
  27. L

    Sequence Question

    U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3) U(r+1) is = (r+1)(r+2)(r+3)(r+4) so U(r+1) - U( r ) = (r+1)(r+2)(r+3)(r+4) - r(r+1)(r+2)(r+3) let (r+1)(r+2)(r+3) = z = z((r+4)-r) = 4z = 4(r+1)(r+2)(r+3) Then if we say V(r) = U(r+1) - U( r ) V(r) + V(r + 1) =...
  28. L

    Sequence Question

    Homework Statement U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3) Hence, find the sum to n terms of the series 2x3x4 + 3x4x5 + 4x5x6 +..... Homework Equations Sequence Knowledge.. The Attempt at a Solution I can't even TOUCH on the problem. Can you...
  29. L

    Feedback Control Systems

    Homework Statement http://img24.imageshack.us/img24/9028/72841137.jpg [Broken] Homework Equations Routh-Hurwitz Stability Criterion The Attempt at a Solution For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough...
Top