Variation Definition and 540 Threads

Homework Statement t²y"-t(t+2)y'+(t+2)y= 2t³ y1(t)=t y2(t)=te^t t>0 Homework Equations w(t)=y1*y2' - y1*y2 g=2t y=-y1∫(gy2)/w + y2∫(gy1)/w The Attempt at a Solution y1=t y1'=1 y2=te^t y2'=e^(t)+ te^(t) w(t)=te^(t)+t²e^(t)-te^(t)=t²e(t)...

Feynman's path integral is: \[ \int {Dx\,e^{{\textstyle{i \over \hbar }}\int {L(x,\dot x,t)dt} } } \] where the Action is: \[ \int {L(x,\dot x,t)dt} \] and the Lagrangian is: \[ {L(x,\dot x,t)} \] Now we are told that as we functionally integrate the path integral in the...

Homework Statement Solve the problem: 4y'' - y = 8e^(.5t)/(2 + e^(.5t)) Homework Equations Particular solution of Y = X*integral(inverse of X multiplied by G) Finding eigenvalues and eigenvectors The Attempt at a Solution This might be a little too messy for anyone to make...

Homework Statement (x2+1)y"+(2-x2)-(2+x)y=x(x+1)2 given 2 associated homogeneous solution are: ex and 1/x Homework Equations this is a question from shaum's outline differential equations chapter on "variation of parameters"The Attempt at a Solution so here what i got... yh=C1ex+C2(1/x)...

Homework Statement Find a particular solution to: y''+4y=20sec(2t) Homework Equations The Attempt at a Solution y''+4y=0 r^2+4=0 r=+or- 2i So, yc(t) = Asin(2t) + Bcos(2t) yp(t)= -cos(2t) ∫ 10sin(2t)sec(2t)dt + sin(2t) ∫ 10cos(2t)sec(2t)dt = -10cos(2t) ∫...

Homework Statement Show that the variation of gravity with height can be accounted for approximately by the following potential function: V(z)=mgz(1-z/R) Where R is the radius of the Earth and z the height above the surface. Homework Equations r=R+z V=-GmM/r F=GmM/r^2 The...

Factor contributes to variation of gravity along latitude is: 1. shape of the earth 2. rotation of the earth gravitational field strength is resolved into two components, (R cos\theta)\omega square, and g' at the poles,\theta =90 degree, therefore, g' = g which is 9.81 at the equator...

Princip stacionary action for propagation of light is apply on thus definition of action: S=\int\!\mbox{d}\tau=\frac{1}{c}\int\!\sqrt{\mbox{d}x_{\mu}\mbox{d}x^{\mu}}=\frac{1}{c}\int\!\sqrt{g_{\mu\nu}\frac{\mbox{d}x^{\nu}}{\mbox{d}\tau}\frac{\mbox{d}x^{\mu}}{\mbox{d}\tau}}\mbox{d}\tau The...

Homework Statement I'm stuck trying to find the coefficient of variation of this calculation: 18.97(+/-0.04) + 0.0025(+/-0.0001) + 2.29(+/- 0.08)= 21.2625. The numbers in parenthesis are the standard deviations for each value. Homework Equations The Attempt at a Solution I...

Hi I am a student trying to figure out how to work ANSYS. The load case never seem to work would appreciate any help. Here is my problem. Two cylinder materials, as shown. The dimensions don't really matter all too much. I then want to have the initial temp at 0 then ramped to 1000 and...

Define "variation" to a beginner How do you define the word "variation" "variability" to a complete beginner, like myself. For Example, I understand 'R' explains how strong the linear relationship between the change in X and Y. But sometimes, let's Say R=.91, people will say the linear trend...

Allright, I understand that we need two solutions to be able to apply the method like y_{1} and y_{2} Problem gives 1 of them or let's you find only that 1 solution. But I can't apply the method since I don't have the other solution. The method I know is: u_{1}'(x)y_{1}(x)+u_{2}'(x)y_{2}=0...

Homework Statement I have to solve the following differential equation by the "variation of parameters" method.Homework Equations \frac{dy}{dx}x +2y = 3x The Attempt at a Solution The associated homogeneous equation of the initial equation is: \frac{dy}{dx} = -2x^{-1}y So \frac{1}{y}dy =...

Homework Statement A sequence b_n is said to be of bounded variation if the series \sum_{n=1}^{\infty} |b_{n+1} - b_n| converges. Prove that if b_n is of bounded variation, then the sequence b_n converges. Homework Equations The Attempt at a Solution If b_n is of bounded...

Dear all, I need a suggestion for my work. I have to measure the variation of some optical features of a material in presence and absence of a magnetic field. Hence, I need to “switch on” the magnetic field in a given instant time, to record the signal an then ““switch off”, or even to change...

Homework Statement Given that x, x2 and 1/x are solutions of the homogeneous equation corresponding to: x^3y''' + x^2y''-2xy'+2y=2x^4 x>0 determine a particular solution. Homework Equations The Attempt at a Solution I'm trying to solve this problem using three...

Hi, I understand the thumb rule that " the pressure exerted by ten metres depth of water is approximately equal to one atmosphere". Is it applicable for pneumatic systems too ?? that with 10 m head difference in air pressure lines there would be 1 bar difference in pressure between the ends...

Hi everyone I am teaching myself QFT, and am currently learning Lagrangian Field Theory. Here is a question I am trying to solve, and I am not absolutely sure if my solution is correct because I am new to this notation and material. I would be grateful if someone could go over it and let me...

Tesla Turbine, variation Just an observation from my shop a couple of weeks ago. Something I have done a few thousand times in my life, and for the first time took notice of what was happening. Turning the switch of my bench grinder on, the need to use the wire wheel for cleaning a small...

Ok here's my problem: 1. Solve the inhomogeneous second order de: x^2y" - 3xy' + 4y =x^4 2. Worked: y(p) = 1/4*x^4 Given: y(1) = x^2 y(2) = log(x)*x^2 3. I just need help getting the roots of the given de so i can determine y(h) of this de. As...

I basically need a function that will animate a chain necklace. Think of the necklace as having three square links on each side with a central medallion. I need this to swing like an actual necklace. My biggest problem with this is the fact that I don't have a standard for gravity...

Let F and f be functions of the same n variables where F describes a mechanical system and f defines a constraint. When considering the variation of these functions why does eliminating the nth term (for example using the Lagrange multiplier method) result in a free variation problem where it...

First time poster, so please feel free to leave any comments of a general nature. I'm hoping to get a further insight on the derivation of the variation of parameters method used in ordinary differential equations to solve linear second order equations. I understand were looking for a...

Hey all, this is a little confusing, because the "variation of parameters" that I have been taught in class is different then what I find in most texts... I have y''' + y' = tan(x) Most textbooks use the wronskian and work from there, what I was taught to do is set it up as the...

This is what a book says - “The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. Thus, the field lines are close together where the electric field is strong and far apart where...

Homework Statement http://img27.imageshack.us/img27/6083/variationofparametersfop.jpg

I am trying to find a clear answer as to why elements' weights vary, when their makeup are of the same protons, electrons, and neutrons? For example, H = 1.0079 atomic weight, 1 proton + 1 electron Li = 6.941 atomic weight, 3 protons + 3 electrons + 4 neutrons If a neutron = 1 proton + 1...

how does cosmology explain that the creation of the universe was not a perfect uniform event in all directions type thing. I mean if you took a chunk of the universe and looked at it the density of matter wouldn't be uniform some planets are bigger than others and so forth. Maybe I am looking at...

Homework Statement Find the general solution of the following diff. eqn. y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0 Homework Equations General soln - Φgeneral(t) + Φparticular(t) Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t) The Attempt at a Solution I'm solving by...

Homework Statement y''+y=tan(x)+e^{3x}-1 Homework Equations homogeneous solution: y_{hom..}=C_{1}cos(x)+C_{2}sin(x) particular solution: y_{parti..}=v_{1}' cos(x)+v_{2}' sin(x) The Attempt at a Solution v_{1}' cos(x)+v_{2}' sin(x)=0 (1) -v_{1}' sin(x)+v_{2}' cos(x) =...

Homework Statement Find the general solution using the method of variation of parameters of: y''-6y'+9y=(x^-3)(e^3x) I found the roots of the corresponding homogeneous equation to be lamba = 3. So there are repeated roots. My question is, how do I solve a variation of parameter...

Homework Statement A metal wire has a resistance of 8.10 at a temperature of 20°C. If the same wire has a resistance of 11.45 at 90°C, what is the resistance of the wire when its temperature is -20°C? Homework Equations R=R(o)[1+alpha(T-To)] alpha=R-Ro/Ro(T-To) The Attempt at a...

Hello all :) Homework Statement I'm trying to understand the fundamentals of General Relativity, but alas, I seem to be unable to grasp the fundamentals of variational calculus. Specifically, I'd like to prove the following relation for the square root of the negated determinant of the...

Homework Statement Show that variation principle (parameters ci) leads to equations \sum\limits_{i = 1}^n {\left\langle i \right|H\left| j \right\rangle c_j = Ec_i {\rm{ where }}} \left\langle j \right|H\left| i \right\rangle = \int {d\textbf{r}^3 \chi _j^* \left( \textbf{r} \right)\left(...

I am looking for information on the density of a liquid at lower temperatures. I have it at 15C as 725 kg/m^3. The fluid is avgas 100LL. I wish to determine it at lower temperatures. I believe that the change in liquid densitiess is rather small for temperature changes, but I can't verify...

Hi, When using the method of variation of parameters to solve something like; y'' + y' = 2^x I got the aux. equation: r^2 - r =0 which gives the roots r=0,1 How do I find the complementary equation yc?

The Einstein field equations \mathsf{G} = \kappa \mathsf{T} can be derived by considering stationary metric variations of the Einstein Hilbert action, S = \int \mathrm{d}^4x \sqrt{-g} (R/2\kappa + \mathcal{L}_\mathrm{M}). 0 = \delta S = \int\mathrm{d}^4...

Consider, x' = x + 3y^3 y' = -3y I am trying to use the fundamental matrix, F(t), and 3y^3 as my g(t) in order to plug into the variation of parameters formula... Xp = F(t) * \integral{ F(t)^-1 * g(t) } , Am I going about this the wrong way? I am trying to get...

Hi I know that our world is quite unstable and minor changes in these parameters could make the existence of life impossible. However, I am interested in what exactly is going to happen if we start to increase/decrease any of 30 parameters. It is interesting how well-tuned these parameters...

Homework Statement What is the unit of the system-universe temperature variation coefficient? The system is a container holding a mass of water. T The universe I guess is the room temperature. Troom t is time in seconds. \Psi is the temperature variation coefficient. Homework Equations...

What is "Variation of Parameters"? Homework Statement None. General. Homework Equations I don't know. :( ? The Attempt at a Solution ? I am taking a class right now on engineering analysis (which I am finding it to be more like partial differential equations mixed with...

Homework Statement y''+2y'+y = 4t^2 - 3 + (e^-t)/t of course i evaluated the general soltuion to be c1e^-1t + c2te^-1t but now how do you do the right part? i tried y=At^2+Bt+c+1/(Dt+E)*e^-t as a solution but after differentiating it twice and putting it into the eqaution i got...

Question is attached as Clipboard01.jpg I have tried the use Variation of Parameters to solve this question, but I kept getting wrong answer. This is What I get y=(2e^x)(Cos(e^x))+0.5(e^(-x))Cos(e^(-x))-2Sin(e^(-x)) This is the right answer: y=-Sin(e^(-x))-(e^x)Cos(e^(-x)) Procedure is...

I was reading about the principle of least action and how to derive Newton's second out of it. at a certain point I didn't follow the calculations, so the author defines a variation in the path, x(t) \longrightarrow x'(t) = x(t) + a(t), a \ll x a(t_1) = a(t_2) = 0 Now, S...

As the name suggest, this problem is an undetermined coefficients problems where variation of parameters is necessary to solve. As with my previous question; This is not a homework problem, but it is out of the textbook so I figured this would be the appropriate place to ask if I am doing it...

I recently got this as an idea for an interesting independent project. I had planned to do the experiment using the four point method of resistance measurement, but I'm stuck on figuring out just what materials I might need to use. I intend to use the basic high school equipment, nothing too...

What role do you think variations play in the process of evolution?

So the problem I am working on is.. A 100 cm long copper wire of radius 0.45 cm has a potential difference across it sufficient to produce a current of 5.0 A at 20°C. Find a) What is the potential difference. b) If the temperature of the wire is increased to 200°C, what potential difference is...

Homework Statement Let y(x) represent the path of light through a variable transparent medium. The speed of light at some point (x,y) in the medium is a function of x alone and is written c(x). Write down an expression for the time T taken for the light to travel along some arbitrary path y(x)...

Homework Statement This is the problem 8.10 from Levine's Quantum Chemistry 5th edition: Prove that, for a system with nondegenerate ground state, \int \phi^{*} \hat{H} \phi d\tau>E_{1}, if \phi is any normalized, well-behaved function that is not equal to the true ground-state wave function...