Second order Definition and 570 Threads

Someone can explain me how to get the general solution for this system of ODE of second order with constant coeficients: \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} \frac{d^2x}{dt^2}\\ \frac{d^2y}{dt^2}\\ \end{bmatrix} + \begin{bmatrix} b_{11} &...

Homework Statement A weight of 8 pounds extends a spring 2 feet. It's assumed that the damping force that acts on the system is equal (number-wise) to alpha times the speed of the weight. Determine the value of alpha > zero so x(t) is critically damped. Determine x(t) if the weight is liberated...

Hello everyone, What does it means first and second order of pressure measurement value? Whats the main difference?

I have attached an image of a question I am trying to do, I want to find the differential equations that describe the second order system in the image. I know for a spring, potential energy = 1/2.K.x (where k is the spring constant, and x is the distance the spring is stretched). I know that...

Hey! :o I have to find the Taylor expansion of second order of the following functions with center the given point $(x_0, y_0)$. $f(x, y)=(x+y)^2, x_0=0, y_0=0$ $f(x, y)=e^{-x^2-y^2}\cos (xy), x_0=0, y_0=0$ I have done the following: The Taylor expansion of second order of $f...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

Homework Statement y′′=−20⋅4x^3 Homework Equations Undetermined coefficients method The Attempt at a Solution so at first, solving the associated homogeneous equation I find the fundamental set of solutions to be: y1=1 and y2=x. I know that these are correct. Now for the part that confuses...

Hello everyone; i'd like some help in this problem : i want to solve num this differential equation { y"(t)+t*cos(y)=y } by the Taylor method second order expansion. i first have to make this a first order differential equation by taking this vector Z=[y' y] then we have Z'=[y" y'] which equal...

When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##? \frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...

I have a second order differential equation of the form (theta is a function of time): \theta ''=F\left(\theta ,\theta '\right) Turning them to two first order equations I get: \begin{cases} \theta '\:=\omega \\ \omega '=F\left(\theta ,\omega \right) \end{cases} And here's the algorithm...

I'm a little stuck getting started on this question. $$y''+\tan(x)y=e^x$$ with $$y(0)=1,y'(0)=0$$. I know the existence and uniqueness theorem for an nth order initial value problem How do I apply the theorem?

Homework Statement So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!) I am asked to solve this differential equation: y''+y'-2y=0 Homework Equations I know for a second order differential equation I can solve for the roots first. If...

Whenever the second order derivative of any physical quantity is related to its second order space derivative a wave of some sort must travel in a medium, why this is so?

Homework Statement Find the general solution. Homework Equations y"+y=x2sin2x The Attempt at a Solution Characteristic equation would be: m2 + 1 = 0 So,m2 = -1 Therefore, m = i or m = -i. Complementary function would be : Asinx+Bcosx where,A and B are constants respectively. If I write...

Hi , I have tried solving the following system of ODE's (eq1 attached) using Matlab. first i reduced it into a system of four 1st order ODE's (eq2 attached). thani tried to solve it using ode45() in the following manner: function xprime = Mirage(t,x); k=2; xprime=[x(1)...

Homework Statement Find: Homework Equations The Attempt at a Solution

I've been thinking about something recently: The notation d2x/d2y actually represents something as long as x and y are both functions of some third variable, say u. Then you can take the second derivatives of both with respect to u and evaluate d2x/du2 × 1/(d2y/du2). Now I think it's also...

In the equation regarding an array of masses connected by springs in wikipedia the step from $$\frac {u(x+2h,t)-2u(x+h,t)+u(x,t)} { h^2}$$ To $$\frac {\partial ^2 u(x,t)}{\partial x^2}$$ By making ##h \to 0## is making me wonder how is it rigorously demonstrated. I mean: $$\frac {\partial ^2...

if I consider a circuit consisting of a capacitor, an inductor and a resistor and using kirchhoffs voltage rule for the circuit i come up with the following L(Q''(t)) + R(Q'(t)) + (Q(t))/C = 0 I solve for the roots using a characteristic equation of the form LM2 +MR +(1/C) = 0 solving this for...

Homework Statement I'm taking an online introductory chem course, and while explaing the failure of classical mechanics to describe electron behavior, the teacher brought up the following ode which is based on Newton's second law and coulombs law: -e^2/4(pi)(epsilon-nuaght)r^2=m(d^2r/dt^2)...

Homework Statement Solve the following system of differential equations: ##y''(x) = y'(x) + z'(x) - z(x)## ##z''(x) = -5*y'(x) - z'(x) -4*y(x) + z(x)## 2. The attempt at a solution I converted the two second order equations to 4 first order equations by substituting: ##g(x) = y'(x)## and...

Homework Statement u'' + w20*u = cos(wt) w refers to omega. Homework EquationsThe Attempt at a Solution I'm not sure where to begin on this. For starters, it's a multiple choice problem, and all the answers are given in terms of y, so I'm not sure if u is supposed to replace y' or something...

Homework Statement Solve: \frac{d^{2}y}{dx^{2}} + \omega^{2}y = 0 Show that the general solution can be written in the form: y(x) = A\sin(\omega x + \alpha) Where A and alpha are arbitrary constants Homework EquationsThe Attempt at a Solution I know that I will need to change variables for...

Homework Statement y'' + 4y = t2 + 6et; y(0) = 0; y'(0) = 5 Homework Equations The Attempt at a Solution So, getting the general solution, we have r2 + 4 = 0, so r = +/- 2i So the general solution is yc = sin(2t) + cos(2t) I then used the method of undetermined coefficients to figure that...

Homework Statement Homework Equations Here is the technique I am using: The Attempt at a Solution [/B] I understand how to solve the problem using the technique provided by the solution but I was wondering where I messed up in the technique that I used. I prefer the second...

Homework Statement y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5 Find the exact solution of the differential equation. Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...

Homework Statement This is not the exact problem that I want to solve but I will use this as a guidance tool: ##y'' - (y')^2 + y^3 = 0## where y is the function of x 2. The attempt at a solution I tried doing a substitution ##u(x) = y'(x)## which leads to ##u' - u^2 + y^3 = 0## where both u...

I'm having a lot of trouble with this problem. I'm also having a lot of trouble inputting it into LaTeX. I hope you can follow even though the markup isn't good. I'm trying to find a formula for the general solution of $ax^2y''+bxy'+cy=0$ where $y=x^r\ln(x)$ when $(b-a)^2-4ac=0$; using...

Im writing a program that calculates the trajectory of a particle in an arbitrary force field. the force field is a vector function of position (x, y, z) AND velocity (x', y', z'). Rk4= runge kutta forth order method Please help. Thanks!

Edit:whoops wrong forum mods please move 2nd edit: I just had dinner then got back on the computer, input some points and saw a beautiful elipse.(complete with a fascinating flower petal design due to inaccuracies) Weird lol! No idea why it wasnt working before Now to implement RK4 bwahahaha...

For twice differentiable path x:[t_A,t_B]\to\mathbb{R}^N the action is defined as S(x) = \int\limits_{t_A}^{t_B} L\big(t,x(t),\dot{x}(t)\big) dt For a small real parameter \delta and some path \eta:[t_A,t_B]\to\mathbb{R}^N such that \eta(t_A)=0 and \eta(t_B)=0 the action for...

Homework Statement Hello all. I'm currently attempting to prove the central limit theorem using a simple case of two uniformly distributed random variables. Aside from being able to solve it using convolutions, I also wish to solve it by using the Dirac Delta function. That aside, the integral...

Hi, all. While solving a second order linear differential equation why do we have to use linear independent but two solutions. For example, when solving y''- y = 0 , y(0) = 5 and y'(0) = 3 , we use ex and e-x and then we write y = c1*ex+ c2*e-x-

Question about Solutions of second order linear PDEs I don't have very much formal knowledge of this topic, this is something I have been thinking about, so excuse me if my notation is off. I have a question about second order linear PDEs, do all have a separable solution? It seems that we can...

hey guys, i have a question regarding bode plot g(s)= 1/(s2+4) i did get the magnitude plot correct but i am unable to understand the phase plot. by calculating on paper i got 0° but in MATLAB it changes from -360° to -180° i haven't understood how the initial phase is -360 which...

Homework Statement find the solution to: \frac{\partial^{2}u}{\partial x \partial y} = 0 \frac{\partial^{2}u}{\partial x^{2}} = 0 \frac{\partial^{2}u}{\partial y^{2}} = 0 Homework Equations theorem of integration The Attempt at a Solution now from a previous question I...

I would like to know how do we solve d2x/dt2 = k' where k' is a constant i.e the task is to find x as a function of time ? One way to approach this is to rewrite it as vdv/dx = k' where v=dx/dt and first find find v as a function of x and then rewrite v as dx/dt and then find x as a function...

Gödel-numbering (in its broadest meaning, not necessarily the one Gödel used): On one side, it would seem that an assignment of a symbol to a number is just a first order function, and the recursion set up to translate a formula into numbers would be first-order, but on the other hand the...

A second order differential equation form d2y/dx2 = f(x,y,dx/dy) How do I read the language on the right hand side?

By combining the two equations i should be able to solve for u' and get rid of u'': u_(i-1) = u_i + (-h)*u' + 1/2 * (-h)^2 * u'' + O(h^4) u_(i-2) = u_i + (-2h)*u' + 1/2 * (-2h)^2 * u'' + O(h^4) But i keep getting stuck and can't come up with the answer below. Can anyone help me please...

Dear all, I have posted a similar question in another forum and the general consensus seems to suggest that it is not possible to symbolic solve a system of coupled second order different equation with damping (dissipation) and driving forces. However, I have found in many papers and books...

Hi, I have looked everywhere. Can someone please point me in the right direction for solving a system of ODEs with variable coefficients? I managed to solve such system with constant coefficients.

Here is the question: I have posted a link there to this thread so the OP can view my work.

How do we solve a system of coupled differential equations written below? -\frac{d^2}{dr^2}\left( \begin{array}{c} \phi_{l,bg}(r) \\ \phi_{l,c}(r) \\ \end{array} \right)+ \left( \begin{array}{cc} f(r) & \alpha_1 \\ \alpha_2 & g(r)\\ \end{array} \right).\left( \begin{array}{c}...

Homework Statement http://books.google.co.uk/books?id=93b3cjVJ2l4C&lpg=PA135&ots=8OtqgKwrQ2&dq=%22Two%20particles%20are%20connected%20by%20a%20spring%20of%20spring%20constant%20k%22%20and%20zero%20equilibrium%20%20length&pg=PA136#v=onepage&q&f=false Homework Equations All in the link...

Homework Statement Attached. If you don't mind I'd like to go through each part of the question to make sure I've understood correctly. Thanks a lot :smile: Homework Equations F=qE F=(γq^2)/(d^2) F=Kx Taylor/Maclaurin (?) The Attempt at a Solution So for part (a) I know that...

Hey, I'm not sure how to even approach this problem. It's not a simple ODE. Basically, I want to find the solution for Θ in terms of ε. The equation is \frac{1}{ε}*\frac{d}{dε}*(ε*\frac{dΘ}{dε})-β^{2}Θ=0 I tried to move the B^2 to the other side and I wasn't able to solve it that way. I...

Homework Statement For second order circuits, do you apply kcl/kvl in the circuit when the switch is open or closed to find the differential equation for complimentary solution? For example for the circuit attached (the circuit has been operating for a long time with switch closed prior...

Homework Statement Solve: [ d^2y1/dx^2 ] = [ a -a ] [ y1 ] [ d^2y2/dx^2 ] [ -a a ] [ y2 ] A = [ a -a ] [ -a a ] Homework Equations Everything required is in (1) above The Attempt at a Solution Reduce to 1st order system M = [ 0 I ] [ A 0 ] Hence, M = [ 0 0 1...

This is a problem from Boyd Nonlinear Optics chptr 1 problem 2. Homework Statement Numerical estimate of nonlinear optical quantities. A laser beam of frequency ω carrying 1 W of power is focused to a spot size of 30μm diameter in a crystal having a refractive index of n =2 and a second order...