Second order Definition and 602 Threads

http://www.math.northwestern.edu/~clark/285/2006-07/handouts/lin-constraint.pdf It's actually proof of finding sign definiteness of quadratic form with linear constraints with sign of submatrices of bordered hessian. The proof is from page 2~page 3. I have 2 questions: 1. From about...

Homework Statement http://img534.imageshack.us/img534/9687/rlc.png Cannot do this question, the first part confuses me when it asks to find an equivalent Parallel circuit. My first instinct was to try to add the capacitor and inductor and 40k Resistance together to create an RLC series...

hello, I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a...

Homework Statement if u=f(x,y) where x=e^s*cost and y=e^s*sint show that (d2u/dx2)+(d2u/dy2) = e-2s[(d2u/ds2)+(d2u/dt2) Homework Equations chain rule relevant here for du/ds and du/dt is du/ds=du/dx*dx/s+du/dy*dy/ds and replace s with t for du/dt The Attempt at a Solution...

Solving second order linear homogeneous differential equation! HELP!? Solve the second order linear homogeneous differential equation with constant coefficients by reqriting as a system of two first order linear differential equations. Show that the coefficient matrix is not similar to the...

Homework Statement Let X(t), -inf< t < inf, be a second order process. Show that it is a second order stationary process if and only if mu(t) sub x is independent of t and r(s,r) sub x depends only on the difference between s and t. Show that is a second order stationary process if and...

Homework Statement This question concerns the second-order differential equation dy^2/dx^2 -4(dy/dx) + 5y = 25x - 3e^2x. Find the solution of the differential equation that satisfies the initial conditions y=0 and dy/dx= 0 when x=0. Homework Equations The Attempt at a Solution

hi. I can't figure out this question: d2y/dx2 - 2 dy/dx - 3y = x (i) find complementary function (ii) find particular integral (iii) using (i) and (ii) find the general solution (iv) find the solution that satisfies the initial conditions: y=2/9 at x=0 and dy/dx=-13/3 at x=0 i...

Hi. I have to solve this: y''-3y'+2y=e^x, Using the replacement y=\phi y_1 being y_1 a solution of the homogeneous differential equation. I can't do it "traditionally", I have to use this method. So I have to solve that \phi ''y_1+ \phi ' \left[2y_1'+Py_1] \right]=e^x So, this is what I...

Hi there. I had some trouble trying to solve this: y''+y=\cos x +3\sin 2x (1) At first I just found the solution for the homogeneous equation: y_h=e^{\lambda x} \rightarrow \lambda^2+1=0 \rightarrow \lambda_1,\lambda_2=\pm i Then y_h=C_1\cos x+ C_2 \sin x So I've tried to find the particular...

Homework Statement I have this problem, which says: If the graph of one solution for the equation y''+P(x)y'+Q(x)y=0 is tangent to the x-axis in some point of an interval [a,b], then that solution must be identically zero. Why? I've tried to do something with the general expression for the...

Hey guys I'm just wondering if I'm on the right track for the problem. I have started analysing the circuit, but I'm really unsure of my method of analysis. Did I use the formulas correctly? :confused: The circuit switches from position "a" to position "b" at t=0 and I'm trying to fined...

I am doing a spring mass problem. Unfortunately, I'm not proficient in Tex so this won't be as neat as it could be. Data: m1=1, m2=1; k1=0, k2=2, k3=0 Stiffness matrix: -(k1+k2) k2 k2 -(k2+k3) 1 0 * x1'' -2 2 * x1 0 1 x2'' = 2 -2 x2 From that, I...

Homework Statement I'm trying to solve a second order ODE for y(x) to show that the solution is y(x)=sin(x)/x. We've been told to use the substitution y(x)=h(x)/x. I've got to the stage of solving for h(x), arriving at h''(x)=-x. Using the general solution, h(x)=A sin(x) + B cos(x) and...

We are doing mass spring problems that stem from second order ODE's. I think my lack of linear algebra is hurting me once again in this section so any help would be greatly appreciated. We are using a stiffness matrix of K = [ -(k1+k2), k2 (row 2) k2, -(k2+k3)] Our first problem has the...

Dear All I'm stuck on something that seems to be contradictory. I was under the impression that the further the 2 closed loop poles are in a 2nd order system to the left of the root locus, the higher the damping. Surely high damping means longer rise time? But other sources say that the...

Homework Statement I'm given two equations first (d^2)*r/dt^2 - r((d*theta/dt)^2)= (-A)/r^2 --- this is a non linear second order differential equation second (r^2)*((d*theta)/dt)=B B and A are...

Homework Statement Solve the following second order linear differential equation d2x/dt2 + x = 2 cos(t) subject to the initial condition x(0) = 0 and dx/dt (0) = 0. What type of motion do you find? Homework Equations The Attempt at a Solution I don't know where to start

Homework Statement Given a second order differential equation: y'' + P(x)y' + Q(x)y = 0 If y1(x) and y2(x) are linearly independent solutions of the DE, what form does Abel's Equation give for W(y1(x), y2(x))? If we assume that one solution y1(x) is known, what first order DE results from a...

Homework Statement http://www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip3-27.pdf Example 7. Not this question in particular, but it shows what I'm talking about. I understand how they get the first partial derivative, but I'm completely lost as how to take a second one. I have tried...

This is from an advanced college physics class, and I'm only in a Calc 1 right now. I've finished the whole problem except for this last part, which deals with a second order differential equation, which I don't know how to do yet. Homework Statement Givens: B, L, A, m, σ, θ (all are...

I am stuck and after several attempts, have made little progress. Homework Statement Solve: (x'-t)x''-x'=0 The Attempt at a Solution I know that the dependent variable x is missing. Therefore, I substitute x'=p and x''=p', giving me, pp'-p't-p=0. However, here I get stuck. If I try to...

Hey folks I'm looking for a way to find the characteristic equation for a second order coupled system of differential equations such as... \ddot{x} + A\dot{y} + Bx = 0 \ddot{y} + C\dot{x} + Dy = 0 Where x and y are functions of time. I know I can solve it by setting x and y to standard...

Homework Statement A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient.Homework Equations I understand...

Homework Statement 22e^{2t}=y''+8y'-9y Homework Equations The Attempt at a Solution The directly previous question to this was the same but homogeneous, i.e. the 22e^(2t) was replaced with a 0. So I know the general solution to the homogeneous ode is C_1e^t+C_2e^{-9t} I know that r(x)=...

Homework Statement 22e^{2t}=y''+8y'-95 Homework Equations The Attempt at a Solution I've been reading a textbook on this and think that I should use "method of undetermined coefficients" I know r(x)=ke^{\gamma*x} so y_p(x)=Ce^{\gamma*x} The trouble is after reading the entire chapter I...

Homework Statement A particular solution of y'' + 4y = tanx Answer choices are: (a) 1/2*cos(2x)ln|sec(2x)+tan(2x)| (b) -1/2*cos(2x)ln|sec(2x)+tan(2x)| (c) 1/2*sin(2x)(ln*cos(x)+x*sec(2x)) (d) 1/2*sin(2x)(ln*cos(x)-x*sec(2x)) (e) none of the above Homework Equations The...

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...

Homework Statement This is NOT a homework problem, but it is similar. Anyway, let's say we have: y''+3y' = 2t^4 This is easy to solve by hand. For the particular solution you get: Yp = At+Bt^2+Ct^3+Dt^4+Et^5 Now, to solve for the coefficients, you can solve them by hand, or you can...

Homework Statement What is the value of a such that the solution of the initial-value problem satisfies limx->infinity y(x) = 0? y''+y'=e^(-x), y(0)=1, y'(0)=a Homework Equations The Attempt at a Solution Not sure what to do with the missing y term... yp=Ae^(-x), y'p=-A^(-x), y''p=A^(-x)...

There seems to be a good source here: http://www.cs.cf.ac.uk/Dave/AI2/node194.html But my problem is understanding the summation. What I am trying to do is calculate ellipticites and orientation angles of images using their second order moments of inertia. My images are in matrix...

Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,

What is the difference? I used to assume First order was a Single DOF system and a Second order was a 2 DOF system. Can anyone give me some clarity. Thanks

Hi all, I've come across this forum when searching for solution to my problem and I found that the community is extremely helpful :) I was working on my college project when I came across the equation below. Homework Statement Z = -0.0006*X^2 + 0.0004*X -0.0008*Y^2 - 0.0006*Y + 0.956...

Dear All, I am trying to solve the following system of PDEs \frac{\partial{A}}{\partial{t}}= a_{2}\frac{\partial{{^{2}}A}}{\partial{x^{2}}}-a_{1}\frac{\partial{A}}{\partial{x}}-a_{0}A+b_{0}B \frac{\partial{B}}{\partial{t}}=...

Hi, I am trying to derive the general transfer function for a second order dynamic system, shown below: \frac{Y(s)}{X(s)}=\frac{K\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} In order to do this I am considering a mass-spring-damper system, with an input force of f(t) that satisfies the...

Hey, I feel kind of stupid for asking this, but how does one solve an ODE of the form y'' = 0 I know it's Ax+B=0 but I forgot how I got there. Cheers,

I've tried and failed to search for this on the forum, so apologies if this has been answered many times before. Given a variable u which is a function of x and y: u = u\left(x,y\right)\\ is it possible to solve the pde: Au_{xx} + 2Bu_{xy} + Cu_{yy} = D\\ The knowns are: The real...

Homework Statement i'm supposed to find the general solution of the equation: y'' + 3y' + 2y = e^x + e^-x Homework Equations I have no problem with solving this equation however, i am confused with the step they are taking in the solutions (circled)...

Homework Statement In aerodynamics, one encounters the following initial value problem for Airy’s equations: y''(x) + xy = 0, y(0) = 1, y'(0) = 0 Using the Runge-Kutta method with h=0.005 and determine values between x=0 and x=10 sufficient to sketch the relationship...

Hi, could anyone tell me what methods I would need to solve this system: y\frac{d^2 y}{d\lambda^2}+\left(\frac{dx}{d\lambda}\right)^2-\left(\frac{dy}{d\lambda}\right)^2=0 \frac{y}{2}\frac{d^2x}{d \lambda ^2}-\left(\frac{dx}{d\lambda}\right)\left(\frac{dy}{d\lambda}\right)=0 I...

Hi I need to find the solution of d^2y/dx^2 + 2x(dy/dx) = 0 I've solved it in Maple and get that y=a*erf(x)+b but I have no idea how to arrive at this answer! Any help would be great, thanks.

Homework Statement The circuit below (please see attactment) shows an RLC filter circuit whereby RC = 1/2 and LC = 1/16. Determine the differential equation that describes the relationship beween the input voltage Vi(t) and output voltage Vo(t). If the initial conditions of the capacitor and...

Homework Statement I need to find the solution to x'' + cx' = f(t), for a general f. Homework Equations The Attempt at a Solution Obviously first I solve the homogeneous part to give me A + B*exp(-ct). I also know that the particular solution is written as (1/c)int((1-exp(c(s-t))f(s))ds...

Hi, I have a problem in calculating the second order correlation (coherence) from the master equation for the operators \sigma and a a[+][/SUP] , because I don't know if <aa^{+}a^{+}a> can be factorized to<a><n><a>. I want to do this calculation directly from the density matrix solution. thanks

Homework Statement The equation is x'' - m2x - m2b = 0. m and b are constants. x'' is the second derivative of x, with respect to time. Homework Equations The Attempt at a Solution When I did a differential equations course, I was taught to find the characteristic equation of the differential...

Homework Statement Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2 Homework Equations - The Attempt at a Solution First I did a change of variables: Let u = e^(-t) Then du/dt = -e^(-t) dx/dt = dx/du*du/dt = -e^(-t)*dx/du d2x/dt2 = d/du(dx/dt)du/dt =...

y1 and y2 are solutions to the ODE L[y]=0=y''+p(x)y'+q(x)yWhat can you conclude about p(x), q(x) and the solutions on the interval I if i) W(x) = 0 for all X on I ii) W(x) = c for all X on I, c =/= 0 --- W(x) = y_1'y_2-y_1y_2' = C*e^{\int{p(x)}} i) W=0 so y1'y2=y1y2' And y1 and y2 are...

Homework Statement y''(x-1)-xy'+y=x2-2x+1 The Attempt at a Solution I don't even know how to start this, Don't know what substitution to do.

first order system DE --> second order Homework Statement Find a second-order DE for x alone that is equivalent to this system. Homework Equations dx/dt = 2x-y dy/dt = -x The Attempt at a Solution I honestly have no clue where to start; in class we pretty much only stuck to...