Constants Definition and 486 Threads

Homework Statement yy''+(y')2 = 0 Homework Equations yv(dv/dy)+v2=0 The Attempt at a Solution Variable separable when solving for the first step the result is: - ln |v| = ln |y| + C1 Now, I've looked at the remainder of the solution with a few other sources and the cause of...

Homework Statement What are the cases in which constants of integration can and cannot absorb terms and operations and just be redefined as c. Homework Equations The Attempt at a Solution As long as I keep redefining my constant of integration I can say -c=k ac=k where...

Homework Statement Extending the Taylor approximation to higher-order terms in high-loss materials. Consider a lossy medium having a finite conductivity a but, for purposes of this problem, no laser susceptibility Xt. First-order expressions for the propagation coefficient ft and the...

Homework Statement How can one simply let C=lnk? Thus changing y=\pm\sqrt{ln(t^{2}+1)+C} to y=\pm\sqrt{ln[k(t^{2}+1)]} Homework Equations None The Attempt at a Solution I know they are both arbitrary constants, are there restrictions on the allowed values of the constants? Actually I...

There's a specific problem I'm doing, but this is more of a general question. The setup is a cylinder of mass m and radius R rolling without slipping down a wedge inclined at angle \alpha of mass M, where the wedge rests on a frictionless surface. I've made the Cartesian axis centred at the...

Homework Statement From the differential equation by eliminating the arbitrary constant from the equation (y - b ) ^2 = 4 (X-a ) http://www7.0zz0.com/2013/02/02/21/747681463.png

Homework Statement I'm attempting to solve the constants that are attained after using separation of variables for a solid permeable prolate spheroidal core wrapped with N turns of wire using boundary conditions. H^{1}_{\delta} inside core H^{2}_{\delta} insulation H^{3}_{\delta}...

Is it the case that the laws we have set for our universe and the proportionality constants which help define those laws are 'set in stone'? If our universe is changing all the time, (i.e. accelerating, expanding) is it not the case that these laws could change over time? Does the entropy of...

I noticed this on the wikipedia page of the big bounce: " All the so-called fundamental physical constants, including the speed of light in a vacuum, were not so constant during the Big Crunch, especially in the interval stretching 10−43 seconds before and after the point of inflection. "...

Homework Statement Consider the following equality: (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V If I rearrange the equality so that I write: (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? What variables will be constant in each side? I'm having some trouble in a few thermodynamics problems because...

Homework Statement A 10g marble is launched horizontally from a spring of K = 20 N/m. If the marble ended up with a launch speed of 40m/sec, how much (in cm) was the spring compressed by?Homework Equations F=kx E=\frac{1}{2}kx^2 The Attempt at a Solution To find how much the spring was...

Homework Statement eliminating c1 and c2 from y, y' and y'' to create a differential equation Homework Equations I have the equation y = (c1 +c2x)e^x y' = c2e^x +(c1+c2x)e^x y'' = c2e^x + c2e^x + (c1+c2x)e^x) (from product rule) The Attempt at a Solution I'm just not sure how to...

Given H=p^2/2 - 1/(2q^2) How to show that there is a constant of motion for this one dimensional system D=pq/2 - Ht ? I tried doing it in my usual way i.e. p'=-∂H/∂q and q'=∂H/∂p and then finding the constants of motion but that doesn't match with what I have to show. Please guide me as...

Homework Statement There's a circuit, with a capacitor C1, Resistor R1, and another capacitor C2. In t=0 ; C1 is charged with 2 V and C2 with 1 V The value of resistor is 1 ohm, C1= 1 F C2=0.5 F Homework Equations Kirchoff voltage law. Capacitor voltage at any given time...

Homework Statement The Taylor expansion of ln(1+x) has terms which decay as 1/n. Show, that by choosing an appropriate constant 'c', the Taylor series of (1+cx)ln(1+x) can be made to decay as 1/n2 (assuming expansion about x=0) Homework Equations f(x)=\sum^{n=\infty}_{n=0} f(n)(0)...

I have always been taught in dimensional analysis that units should cancel out before you log a number. The problem I have, as stated in the title of this thread, is that units don't seem to cancel out when applying bimolecular rate constants to the Eyring equation: ln[(kh)/(kBT)] = -ΔH‡/(RT)...

How can I plot this probability density function using Wolfram Mathematica Keeping the constants the same. ψ*ψ= A^2 (x^2)exp(-2a(mx^2/h)) ; where m,a,A,and h are constants and I want the graph in terms of them. I tried: Plot[A^2 *(x^2)*exp(-2a(mx^2/h)),{x,-1000,1000}]

Hi, I'm a new AE Ph.D. student in the field of supersonic mixing and combustion, currently making preparations for ordering equipment necessary to perform Filtered Rayleigh Scattering measurements in our tunnel. At this point, I am implementing a model for predicting the shape of the...

Homework Statement Find the function f(x) such that f''(x) = \frac{1}{x^2}, f(1) = 0 and f(e) = 0 Homework Equations \int f''(x)\,dx = f'(x) + c \int f'(x)\,dx = f(x) + cx + C The Attempt at a Solution f''(x)= \frac{1}{x^2} f'(x)= \int \frac{1}{x^2}\,dx = \frac{-1}{x} + c f(x) = -\int...

Consider the Hamiltonian of Kepler problem H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\frac{\alpha}{|\boldsymbol{r}|}, \qquad \mu>0>\alpha, where \boldsymbol{r}\in M=\mathbb{R}^3\setminus\{ 0 \}, \ (\boldsymbol{r},\boldsymbol{p})\in T^*M and...

Consider the Hamiltonian of Kepler problem H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\frac{\alpha}{|\boldsymbol{r}|}, \qquad \mu>0>\alpha, where \boldsymbol{r}\in M=\mathbb{R}^3\setminus\{ 0 \}, \ (\boldsymbol{r},\boldsymbol{p})\in T^*M and...

Hey folks, Bit of a complex question here, but I'm hoping someone smarter than myself can help me figure this out. I want to make a parabolic curve that is controlled by 2 constants S and T. I know that in y = Ax2 + Bx + C C = S as one of the points I can give from the if statements I'm...

Homework Statement Suppose are h and k are unknown constants. The equations are: -3x-5y-6z=-4 8x+6y-9z=8 19x+17y+hz=k if h≠A then A=? Homework Equations The Attempt at a Solution I know that h is some number so that this system of equations...

Homework Statement There is not really a problem, just a question which i am about to ask. The known data is \alpha the fine structure constant \hbar Plancks constant c the speed of light \mu permeability Homework Equations 2\alpha \hbar = \pi^2 \mu_0 c The Attempt at a Solution A paper I...

Hey guys and gals, this isn't actually an assignment of any sort, so I didn't want to put it in the homework section. This is also my first post, though I have been lurking for quite a while, reading the copious amounts of information available here. :p Anyhow, could somebody please elaborate...

Is the statement Ke=k+/k- valid for all equilibrium constants like Ka, Kx, Kp, Kc? All of the expressions I have found for this statement relate Kc, k+ and k- only.

I want to integrate γβγx/(β + x)γ+1 from 0 to ∞ (given β and γ are both > 0) So for large x the integrand is approximately proportional to x-γ So for which values of γ is the integral defined? Surely for any γ > 0 the integrand tends to zero as x tends to infinity? Thanks

why do most modern books claim the divergence of the E field is ρ/ε_{0} but in more classical books, and when you actually derive it mathematically you arrive at 4πρ

For example: tan(pi/2 - pi/4) = (tan(pi/2) - tan(pi/4) ) / 1 + tan(pi/2)tan(pi/4) Which of course comes out to: undefined + 1 / 1 + undefined Does that equal 1, or equal Undefined/No Solution?sorry for the poor formatting, I couldn't find the mathprint symbols for pi and fractions

HAllo everyone, I had a problem with the measurement of young modulus and shear modulus with ultrasonic measurements( pulse-echo overlap technique) For my metallic glasses rods (amorphous material) I used these formula for the calculation: 1. determination Shear modulus: G= ro * v...

Two capacitors have the same plate separation, but one has square plates and the other has circular plates. The square plates are a length L on each side, and the diameter of the circular plate is L. The capacitors have the same capacitance because they contain different dielectric materials...

Find all the values of the constants a and b such that \lim_{x\rightarrow0}\frac{\sqrt{a+bx} -\sqrt{3}}{x} = \sqrt{3} I tried to multiply by the conjugate, but it indeed failed to give me any insight as to how to solve this problem. Could someone possibly prod me into the right direction?

Homework Statement solve the following differential equation: t4x'' - 4t3t' + 6t2x = - 12t - 20 Homework Equations substitution x(t) = tn The Attempt at a Solution this is a Euler equation with the following general solution: x(t) = c1t2 + c2t3 worked out using the above substitution. The...

Homework Statement Hello! I need some help with a problem: Problem: Turbulent flow beteween parallel flat plates. It is defined: [ tex ] \tau = \mu \frac{d\bar{u}}{dy}-\rho\bar{u'v'} [ \tex ] The exercise gives that [ tex ] \tau = a y [ \tex ] and [ tex ] \rho\bar{u'v'} =...

Every book I look at, they state rate = -Δ[A]/Δt = k[A] , for A → B From there, they go on to derive the concentration-time equation. Well, my concern is what if we have: aA → B Shouldn't "a" be accounted for in the derivation. In other words, why don't we derive a more general equation...

What exactly are constants? Are they just used to make the equation work or is there something more meaningful than this? Right now I am studying rate of reactions and they go something like this: rate = k [A]^x [B]^y It seems like k is only there to make the equation work. It would seem like...

Ka = [H+][A-]/[HA] Is the term "[HA]" referring to its initial concentration or its equilibrium concentration?

Homework Statement For an application you require a thin wafer of dielectric with dielectric constant = 12 perpendicular to the wafer. You have available a tetragonal crystal of dielectric ceramic with relative dielectric constants εx = εy = 18. and εz = 10. At what angle to the z axis...

Dielectric constants in different directions -- does this make sense? So I'm trying to analyze a scenario in which I have a plane wave incident (from, say, some medium with permittivity and permeability ε_1 and μ_1), on a plane of a dielectric material that has an anisotropic permittivity: in...

The question gives me a graph of spring 1 and spring 2 (which I will attach to the post) and it asks me what are the springs constants. I have no idea how to find the spring constants. I know that the Potential Elastic equation is (1/2)k(x^2), but I don't know where to start with looking at this...

Hello, I need help trying to simplify the equation below, I believe it should be in terms of x and constants only, no trigonometry. "Simplify arctan(cot(x)), assuming 0<x<pi/2" After many attempted solutions and failures, my most recent attempt is below. let arctan(1/tanx) = u ==> tan...

What are the dissociation constants of NaCl and KCl respectively? I want to determine how much of the salt dissociates in a 1 M solution. Thanks!

I need to find B in terms of F in a finite square well potential I started with -Ae^(-i*K*a) - Be^(i*K*a) = Csin(k2*a) - Dcos(k2*a) and Ae^(-i*K*a) - Be^(i*K*a) = i*K*k2 [C*cos(k2*a) - D*sin(k2*a)] where C = [sin(k2*a) + i*(K/k2)cos(k2*a)]*Fe^(i*K*a) D = [cos(k2*a)-...

Homework Statement How do you integrate this? x-ae-b/x, where a and b are some constants. The Attempt at a Solution I have tried this http://integrals.wolfram.com/index.jsp?expr=x+*+e^%28-1%2Fx%29&random=false Is there a closed form of this?

How many independent fundamental physics constants are there that are not expressed in terms of other constants? What are they? I assume they would include the speed of light, c, and ε0, but μ0 can be left out, the gravitational constant, Plank's constant, fundamental particle masses and...

What are the Values of "Machine Constants" in Excel/VBA? The Fortran code for TOMS Algorithm 691 refers to five "machine constants" belonging to the host computing environment. Two of these are: 1. "The smallest relative spacing", given as "B ** (-T)", where B = base (say 10?), and T =...

Hello, i have the equation F= x + kx^n I am trying to determine the constants k and n? where i have the ranges for F and x is what i am doing correct? log F= logx + logk+ nlogx log F= logx(1+n) + logk ok i would then plot logF vs Log x. if i am correct logk = y intercept and...

Activation energy from a decomposition. Homework Statement . The rate constant for the decomposition of C2H6 is given in the table below. Calculate the activation energy. 105 k/s Temperature/K 2.5 823 4.7 833 8.2 843 12.3 853...

Until now, I have come this far:The differential equation equals the particular part, and the homogene part: x = x_p + x_h The homogene part equals the differential equation when set to zero \frac{d^2x}{dt^2} + \frac{K_p}{A} \times \frac{dx}{dt} + \frac{K_p}{A \times T_i} \times x(t) = 0...

Can someone please help me answer this question and explain the concepts/solution step by step: Prof. W.H Bogus claims that he has prepared a powerful new catalyst that makes it possible to synthesize NH3 with a 70% yield in a reactor operating 500K and 2 atm pressure and having a feed...