What is Variation: Definition and 574 Discussions

A ambiguous variation of Einstein--Hilbert action Variation of EH action is: \delta S_{EH}=\int_{\Omega}{\delta(R\sqrt{-g})dx^4}= \int_{\Omega}{G_{\mu\nu}\delta{g^{\mu\nu}}\sqrt{-g}dx^4}=0, where G_{\mu\nu}:=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R is symmetric einstein's...

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...

Homework Statement You are given that two solutions to the homogeneous Euler-Cauchy equation x^2 \frac{d^2}{dx^2}y(x) - 5x \frac{d}{dx} y(x) + 5y(x) = 0 y1=x, y2=x^5 y''-\frac{5}{x}y'+\frac{5}{x^2}y=-\frac{49}{x^4} changing the equation to standard form use variation of parameters to find a...

hi, I have to calculate total variation of this function: 1 for x< 0 sin(pi * x) for 0<= x <= 3 2 for x> 3 I could not find any example for doing this. Can someone help me ?

Hi, I have a 480 V, 200 kVAr and 60 Hz capacitor bank. I need to move this bank to a location with 390 V and 50 Hz, I wonder what would be the resulting power of the bank. Regards.

how does specific heat of gases vary with temperature? is there an equation to describe it?

Central Limit Theorem Variation for Chi Square distribution? If this question fits into Homework Help, please move it over there. I'm not too sure. I encountered the following problem: Now, this problem seems fairly similar to a simple proof the central limit theorem. I am damn sure...

Homework Statement Find the particular solution to the differential equation using method of variation of parameters: 4y''-4y'+y=16e^(t/2) The Attempt at a Solution Set 4y''-4y'+y=0 then the homogeneous solution is: y= c1*e^(t/2)+c2*te(t/2) set y1= e^(t/2), y2= te^(t/2)...

Homework Statement A rectangular tank is filled with water 2 m deep. At the bottom of one side wall is a rectangular hatch 1 m high and 2 m wide that is hinged at the top of the hatch. a) Determine the force the water causes on the hatch. b) Find the torque caused by the water about the...

Homework Statement t^{2} * y'' - 2y = 3t^{2} - 1 y_{1} = t^{2} y_{2} = 1/tHomework Equations Variation of Params forumla wronskian det The Attempt at a Solution W = t^2 * -t^-2 -[1/t * 2t] = -3 Y = -t^2 * Integral[ (-1/3)(1/t)(3t^2 -1)] + 1/t * Integral[(-1/3)(t^2)(3t^2 -1)] I get an...

I have a question on the integration part of the Variation of Parameters. Given .y''+P(x)y'+Q(x)y=f(x) The associate homogeneous solution . y_c=c_1y_1 + c_2y_2. The particular solution . y_p=u_1y_1 + c_2y_2. u'_1 = -\frac{W_1}{W} = -\frac{y_2f(x)}{W} This is where I have question...

Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...

4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?

Homework Statement Using variation of parameters, find the general solutions of the differential equation Homework Equations y''' - 3''y + 3y' - y = et / t where et/t = g(t) The Attempt at a Solution I know how to solve these types of equations when its a second order, but I don't...

Hey guys, This is my first post on PhysicsForums; my friend said that this was the best place to ask questions about math. Anyways, I have to find the Quadratic Variation of a Poisson Process. My professor doesn't have a class textbook (just some notes that he's found online), and...

Homework Statement f is of bounded variation on [a;b] if there exist a number K such that \sum^{n}_{k=1}|f(ak)-f(ak-1)| \leqK a=a_0<a_1<...<a_n=b; the smallest K is the total variation of f I need to prove that 1) if f is of bounded variation on [a;b] then it is bounded on [a;b]...

1. Show that the variation of pressure with altitude for a planetary atmosphere (assuming constant temperature) is more accurately given by: p = poek(1/r-1/R), where g is taken to vary as 1/r2 (with r being the distance from the centre of the planet), po is the pressure at the surface, R is the...

I was doing some reading and I came across this: http://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures So apparently for the finite case, \max_{x} ( \left| P(x) - Q(x) \right|)\quad \mbox{ is equivalent to}\quad \frac{1}{2} \sum_x {\left| P(x)-Q(x)\right|}...

Hi, I am doing my revision and one of the question got me thinking but I am not sure if I got it right. The question asks what is the effect of variation of steam supply on power output,power factor,armature current and load angle of the synchronous machine. I think reduced in steam...

I was looking at section 7.6 of Longair's Galaxy Formation, and in it, he is talking about the flatness problem, or fine-tuning problem. In it, he shows that if you define a general (i.e. varies with cosmic time and hence with redshift) density parameter \Omega_m for matter by analogy with...

Homework Statement (D^2 + 2D + 1)y = ln(x)/(xe^x) Homework Equations D = d/dx The Attempt at a Solution First I find the roots of the left side of the equation, -1 of multiplicity 2. This leads to y(c) = Ae^(-x) + Bxe^(-x) Substituting A and B with a' and b' and dividing...

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment. Expected Profit: A - 100 B - 120 C - 140 Standard Devi.: A - 10 B - 30 C - 20 I presume to calculate the...

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment. Expected Profit: A - 100 B - 120 C - 140 Standard Devi.: A - 10 B - 30 C - 20 I presume to calculate the...

I am trying to solve the following equation using the variation of parameters method d2x/dt2-(q2Bz2/m2)x=qEx/m I have put x1=cos(t) and x2=sin(t) into the Wronskian method. Can someone tell me if these are the correct functions to use, or should I be using exponential functions. Any...

! Cyclic variation of engine torque If the cylinders fire sequentially according to the fire order 1-2-4-3 What is the pattern of the cyclic variation of each cyclinder engine torque and the resultant engine torque?

Hi all, I m not a physicist but a biological oceanographer. I would like to know how should I consider space-time variations of tiny cells in the ocean? Usually people deal with space and time separately but do not compute the data over a space-time scale (which I believe is important...

Homework Statement In discharge mode, calculate the variation in mass of the compounds of a lead-acid battery if the sufuric acid mass decreases by 294g (3 moles). Homework Equations The semirreactions: Pb \to P{b^{2 + }} + 2{e^ - } 4{H^ + } + Pb{O_2} + 2{e^ - } \to P{b^{2 + }} +...

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...

Homework Statement Using the conservation of angular momentum and Kelper's third law, show that the relative change in orbital period produced by mass transfer is given by 1/P * dP/dt = 3 dM1/dt * (M1 - M2)/(M1M2) Homework Equations L = mu * sqrt(GMa) P^2 = (4*PI^2)/(G(M1+M2)) * a^3...

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...