Linearize Definition and 23 Threads

I am doing an investigation of how much a beam sags, based on the distance from its midpoint. This is my hypothetical equation: The relationship between distance, d and sag, s is not a linear relationship. Below, is the determined relationship between the variables, linearized by natural...

By using the laplace transform: $f(t)=sin(Φ(t))$ I want it in the form: F(S)/Φ(S) The purpose is to linearize it in order to put it into a larger transfer function, so far my only solution is to simplify it using taylor expansion.

<Moderator's note: Moved from a technical forum and thus no template.> Technically the homework question is at graduate level, but the area I'm having trouble on I feel is at an undergraduate level. In the question we studied a particle rotating on a vertical hoop that is also rotating about...

Hi, I'm supposed to linearize this set of data: "Below is a data set which includes information about the motion of the objects in the solar system. Note: the periods are listed in Earth years (time it takes the Earth to complete one orbit around the Sun) and the average distances are reported...

Homework Statement I'm doing a lab report about how the launch angle affects the range of a projectile. Independent Variable Angle of Launch Dependent Variable Range or distance I did an experiment with three trials and here are my results: And then plotted the data. However, it's a...

I am linearizing a vector equation using the first order taylor series expansion. I would like to linearize the equation with respect to both the magnitude of the vector and the direction of the vector. Does that mean I will have to treat it as a Taylor expansion about two variables...

Hello! I'm completing my IB Physics IA and after collecting my data and plotting the raw graph my graph seems to be a negative parabola. In order to linearize it I though one had to square the x-axis data; however I simply get the same graph shape. What am I supposed to do? Only when I plot the...

Homework Statement By taking the natural logarithms of each side, that this equation can be linearized by making a semi logarithmic plot. Identify the variables and state what the slope , and y-intercept would represent. Homework Equations F=Fo*e^-(d/cτ) The Attempt at a Solution I tried...

Homework Statement The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation: rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants...

Homework Statement These are the Points. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51 I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs. 2. The attempt at a solution I know it's a...

For our physics lab we found the magnetic field produced by a magnet at different distances. When graphing the data, it was supposed to produce a linear graph when we plot the field strength against 1/r3. However, my graph doesn't become linear until 1/r5 (however, it does linearize quite nicely...

1. Homework Statement Linearize the euler equations of fluid motion, write as a single partial differential equation for example the pressure pertubation Homework Equations The euler equations of fluid dynamics The Attempt at a Solution Not sure how I would be able to do this.

Have typed the question is latex format, here it is: http://i.stack.imgur.com/grxgI.png

Hello folks, I am attempting to implement an LQR controller to a quadrotor and in order to do this I need to linearize the model's equations about a certain trim point, in this case hover, which makes all initial conditions equal to 0. However I am having a lot of trouble linearizing these...

Homework Statement Linearize the following equation: \dfrac{1}{r} = (\dfrac{2g(\rho - \rho\prime)}{9\eta})(\dfrac{r}{v_{0}}) - \dfrac{K}{R} Here, v0 is the observed velocity dependent upon r, and we are trying to get η and K somewhere in the intercept and slope. So we will try out different...

HI, I have solved the diffusion equation using the central difference scheme. Next, I would like to code this diffusion equation with a nonlinear term added to the equation. The full equation is as follows: dS/dt = Ds * d^2S/dx^2 - aS/b+S Since aS/b+S is a nonlinear term, I need to...

The formula used for linearization is y=(m)(Square root of x) + b correct? How do I find the square root of x if given various plotted data?

Homework Statement Need to linearize the poisson-boltzmann equation to be used later in the problem. I simply have never linearized an equation and searching google didn't really help me understand.Homework Equations http://img215.imageshack.us/img215/2149/eqnq.jpg The Attempt at a Solution...

Homework Statement A problem in classical mechanics, dealing with an object in space collecting mass as it passes through a dust cloud has led me to the following nonlinear ODE. I'm quite sure it is the correct equation, my old man checked it out. But being the engineer he is, he would just go...

Hello! I have got three exercises http://images46.fotosik.pl/55/068c355872bdd5a9.jpg . I was working on second and third and I understand them more or less. Unfortunately I don't know at all how to solve first exercise. I was looking for some materials which may help me to solve it and I found...

Is there anyone that can help me about linearization of the equations around x=teta=0 ? It is a bit urgent. I am waiting answer from the calculus experts.

For this system of differential equations \frac{dx}{dt} = x(0.8 -\frac{0.8x}{3129} - \frac{y}{x+1000}) \frac{dy}{dt} = y(-0.5 + \frac{x}{1000+x}) for all x,y \geq 0 now the equilibrium points are (x,y) = (0,0), (1000,1088), (3129,0) i need to linearize this system such taht i can...