Linearization Definition and 72 Threads

  1. C

    Linearization of function F(t) = t2 /2 + 2t

    Homework Statement Finding the linearization of the function F(t) = t2 /2 + 2t at t = -1. Homework Equations F'(t) = t+2 The Attempt at a Solution F(t) + F'(t)(t-a) -3+1(t+1) = t -2
  2. K

    Linearization Help: y" (t)+ y'(t)+y(t)=u2(t)-1

    urgent help for Linearization Dear All, y" (t)+ y'(t)+y(t)=u2(t)-1 Linearize the system about y(t)=0, u(t)=1, for all t>= 0 can we say that this equation is already linear at the given point which will be y" (t)+ y'(t)+0=1-1 => y" (t) + y'(t)= 0 and no need for linearization.
  3. A

    How Is a Nonlinear Equation Linearized in FEM Software?

    Hi, I am trying to understand an example from a FEM software manual. The manual mentions a nonlinear equation http://aamir-pc:2080/v6.9/books/exa/graphics/exa_eqn00137.gif and this equation is linearized to obtain http://aamir-pc:2080/v6.9/books/exa/graphics/exa_eqn00152.gif .[/URL] Can...
  4. M

    Local Linearization of f(x) = cosx at a = $\pi$/2

    f(x) = cosx, a = \pi/2 since, L(x)=f'(x)(x-a) -f(a) f'(x) = -sinx = -sin(\pi/2)(x-\pi/2) - f(a) I'm stuck as to where to go next, is this even right?
  5. G

    How Can Variables l and T Be Plotted to Determine k from a Graph's Slope?

    Homework Statement How should the variables ( l and T) be plotted to obtain k from the slope of a linear graph? Identify (write out) the constants correstponding to the slope and intercept of the linear graph. Homework Equations l = lambda l = (k/f)*(T/u)^0.5 The Attempt at a...
  6. Q

    Linearization with a Constant Block in Matlab

    Hi All, Homework Statement I have modeled a simple spring mass system in Matlab and trying to use linmod to linearize the system. The system models a mass that hangs from ceiling with a spring and damper. So, the forces that act on the mass are gravity, spring force and damping force. I...
  7. R

    Linearization of a non linear equation

    Homework Statement I'm sure this is easy but I've been looking at it for an hour and can't get anywhere. I have an equation that I need a linear form of. Homework Equations y = a*b*(x1*x22-(x3*x44/c))/(1+b*x1) That's the equation I have to write a linear form of. The Attempt at a Solution...
  8. M

    Linearization of nonlinear non homogenous ODE

    Hi everybody, could anyone help me in the linearization of the following non linear non-homogeneous ODE? A*dy/dt+B*y^(4)=C where A, B and C are constants. y is a function of t. is it possible to reduce this equation to a Riccati equation? do you know any analytical, approximate or...
  9. M

    What is the Linearization Process for Water Tank Systems?

    If you have a water tank with an inflow u, and an outflow v, you have that \frac{dV}{dt} = A \frac{dh}{dt} = u - v. You can now linearize this expression so that you get A \frac{d}{dt}(\Delta h) = \Delta u - \Delta v = (u-u_0) - (v-v_0), where \Delta h = h-h_0. I think I...
  10. B

    Fluid Dynamics, Linearization Question

    Homework Statement Consider an ideal fluid large enough to experience its own gravitational attraction. If the fluid is initially at hydrostatic equilibrium with density \rho_{0} (r) and pressure p_{0}(r) , it can develop small amplitude pressure waves which may be analyzed as follows...
  11. H

    Linearization of ln(7x) at a=1/7

    Homework Statement find the linearization of L(x) at a. f(x)=ln7x, a=1/7 Homework Equations f(a)+f'(a)(x-a) The Attempt at a Solution i got f(1/7)=0 and f'(1/7)=9.12 then shouldn't it be 0+.9.12(x-0)=9.12x?
  12. D

    Linearization of an equation around fixed points

    Homework Statement Find the linearization of the equation y' = y(-1+4y-3y^2) about each of the fixed points The Attempt at a Solution I think this is correct for finding fixed points: Set y' = 0 = y(-1+4y+3y^2), so the fixed points are y = 0, 1/3, 1 What exactly does it mean by...
  13. H

    Do you understand what linearization means?

    do you understand what "linearization" means? Homework Statement Linearization 4x'' + 3 cos(x-y)y'' +2 y^2 sin(x-y) +3g sin (x) = 0 Homework Equations initial condition x(0) = y(0) = 0 The Attempt at a Solution pls tell me the relevant steps to solve this problem.thanx
  14. F

    Linearization and tangent lines

    This is a general question, but what is the difference between finding the linearization and the tangent line to the same curve? And what about at a specific point?
  15. R

    Linearization of f(x)=x^1/3 at a=-64

    Find the linearization of f(x)= x^1/3 at a=-64 so i am trying to use f(x)=f(a)+f'(a)(x-a) f(a)=-4 f'(x)=1/3(x^-2/3) f'(a)=-1/48 so i get -4+1/48(x+64) is that right?
  16. I

    MATLAB Matlab Linearization: Best Approximation Using Polyfit

    Hello, this is my situation: I've got some data from an experiment stored in matlab. So I plot the graph and get a x^2 curve. I plot the loglog graph and see a near-"perfect" line. Now I want to create the best approximation to it (in a least squares sense). I don't want to do that...
  17. D

    Linearization - no idea how to do this

    Can someone point me in the right direction for this problem. I have no idea how to start on this. I know the linearization formula but i don't know if that's what i have to use here. can someone please help problem: You want a linearization that will replace the function over an interval...
  18. M

    Linearizing f(x,y,z) at (1,1,1) for Quick Calculations

    I am linearizing the function f(x,y,z) = tan^{-1}(xyz) at the point (1,1,1). Since f(x_0,y_0,z_0)= \frac{\pi}{4} + \pi*n should I just take the first value or do I have to carry all the solutions through the linearization process? Um, anybody remember this? I can put up some work if it...
  19. S

    Understanding Graphical Linearization: Exploring Linear and Non-Linear Graphs

    Hello everyone, I am stuck on a problem relating to graphical linearization. The way we did it in high school was much easier than here. Anyway here is the question: There are many ways to graph equation (1) d=Vot+(1/2)at^2, depending on the arrangement of the variables d vs t. However...
  20. B

    Linearization of Non Linear Equation

    Ok so here is the problem: You have six steel bearing varying in size and you have their mass and diameter. When you graph the data you see that the mass (in Grams) goes up exponentially as diameter (in cm) goes up. Below is the table of the Mass and Diameters M=.44 D=.4 M=2.04 D=.8...
  21. U

    Local Linearization: Finding the Formula of a Graph

    the question is http://home.earthlink.net/~urban-xrisis/clip001.jpg I got a different answer than what the book says... so I need to find the formula of the graph. H'(3)=f(3)=2 m=\frac{\Delta y}{\Delta x} 2=\frac{\Delta y}{x- \int^3_0 f(t)dt} y=2(x+2) y=2x+4 the book's answer...
  22. D

    Are My Partial Derivatives Correct for Linearization?

    Original question: Let f(x,y) = ln(xy) + yzcos(xz). Find the linearization of f at the point (1,1,pi/2). Use this linearization to estimate the change in the value of the function resulting from moving from (1, 1, pi/2) to (1.1, 1.2, pi/2 + 0.2). I believe the first steps to completing...
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