Coefficients Definition and 753 Threads

The measured pH of 0.100 M HCl at 25°C is 1.092. From this information, calculate the activity coefficient of H+. I tried using the Debye-Huckel equation and got 0.825 but it's not right. I don't know how else to solve for the activity coefficient.

Homework Statement There is an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle θ = 20°. What is the magnitude of the acceleration of the block across the floor if (a)μs = 0.630 and μk = 0.540 and (b)μs = 0.400 and μk = 0.330...

The lifetime of the 32P1/2 to 32S1/2 transition of the Na atom at 5896 angstrom (one of the Na D lines) is measured to be 16.4 ns. What are the einstein a and b coeff? What is the transition moment in debye? What is the peak absorption cross section for the transition in angstrom2, assuming...

The connection \nabla is defined in terms of its action on tensor fields. For example, acting on a vector field Y with respect to another vector field X we get \nabla_X Y = X^\mu ({Y^\alpha}_{,\mu} + Y^\nu {\Gamma^\alpha}_{\mu\nu})e_\alpha = X^\mu {Y^\alpha}_{;\mu}e_\alpha and we call...

Hey all, there is something that has always bugged me in linear second order ODEs. We say that the general solution is: y=C_1e^{r_1x}+C_2e^{r_2x} where r_1 and r_2 are the solutions of the characteristic polynomial. The cases where r1, r2 are real are pretty straightforward. If they are...

Homework Statement I have two spin-1/2 particles and I need to calculate their Clebsch-Gordan coefficients.Homework Equations The Attempt at a Solution I followed the procedure of applying J_- to |{j,m}\rangle and J_{1-} and J_{2-} to |{m_1,m_2}\rangle and comparing them. I got correctly...

Do any of you know just a general range of friction coefficients for tires? I'm working out some braking problems, but can't really find anything searching online.

Homework Statement Given that p(x) is a polynomial defined by (x+1)(x^2+2)(x^4+4)(x^8+8)...(x^1024+1024) and knowing that the coefficient on x^2012 can be written as 2^a, find a. Homework Equations Binomial thereom mabye idk The Attempt at a Solution Tried grouping up terms that...

I'm told that factoring is an important skill in calculus so I am avoiding using the quadratic formula. But for quadratic equations with large coefficients to factor, is there a better/faster way rather than guessing and checking every single combination?

Hi, I am trying to solve the following equation: \Psi(r,t) = \sum_n C_n(t) e^{-i E_n t} \psi(r) to find the C_n(t)s. The system I am modeling is benzene. I can, by Hückel's method, determine the time-independent solution. The apparently obvious transition from time-independent...

Homework Statement For a given periodic function F(x), the coefficients An of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed: An =(\frac{2}{πn})sin(\frac{πan}{λ}) for n≥1 and...

Homework Statement For the differential equation y'' - 4y' + y = 0, (a) Show that if we let x = y' (i.e. x(t) = y'(t)), then this leads to the system: x' = 4x -y y' = x (b) Conversely, show that the system in (a) leads to y'' - 4y' + y = 0 (and x'' -4x' + x = 0 also). Homework...

Homework Statement Fidn the Fourier expansion for f of period 2Pi that corresponds to y=x/3 on the interval [0,2Pi) Im just a little confused about if I am setting up the integration properly. The asymmetric interval is kind of confusing me here. The Attempt at a Solution a0 = 1/Pi ∫ x/3 dx =...

Homework Statement Homework Equations Sum of roots taken one at a time is -b/a Sum of roots taken two at a time is c/a three at a time is -d/a four at a time is e/a The Attempt at a Solution I did part one by solving the two equations...

Thanks for any help! I'm trying to understand the coefficients of a 2d DFT. say we've got this matrix, f(a,b) \left( \begin{array}{ccc} 9 & 1 & 9 \\ 9 & 1 & 9 \\ 9 & 1 & 9 \end{array} \right) I used wolfram alpha's function, Fourier{f(a,b)} and the transform comes back as \left(...

If I wanted to solve this y''+3iy'+y=cos(2t) using undetermined coefficients. and I make the guess y=Ae^{2it} then i find y' and y'' and then solve for A. I get that A=-1/9 then I take the real part when I multiply it to Eulers formula. But when I plug this back into check it...

Homework Statement Show that the imaginary part of the solution of z''+z'+z=te^{it} is a solution of y''+y'+y=tsin{t} The Attempt at a Solution Ok so I first make the guess that z(t)=(at+b)e^{it} then I find z' and z'' and plug it back in and then equate the coefficients of t...

Awhile back A.T. & PeterDonis helped me through several basic confusions on my way to an intuitive understanding of geodesics in curved spacetime. I looked at http://www.relativitet.se/spacetime1.html http://www.adamtoons.de/physics/gravitation.swf...

Ok, so obviously, given some polynomial P(x) of degree r, it has r roots in the complex numbers by the FTOA, and if these roots are u_1, u_2,... it can be written as \begin{array}{l} P(x) = (x - {u_1})(x - {u_2})(x - {u_3}) \cdots \\ P(x) = {x^r} - ({u_1} + {u_2} + {u_3} + \ldots ){x^{r - 1}}...

Homework Statement I want to prove that coefficients of potential are non-negative. i.e. Pij ≥ 0 Homework Equations By coefficients of potential method we know that in a system of conductors the potential on ith conductor is related to charges on conductors by: \Phii = \sum Pij Qj...

I've been fooling around with the Fibonacci sequence for some time and I thought it would be interesting to see what would happen if I made the coefficients in a three variable system of equations follow that sequence. The results are intriguing and enigmatic. I discovered the following...

Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...

what will be the rate of acceleration be when a 10N force is applied to a 7.0kg block of wood resting on a table with a coefficient of friction equalling 0.45? ok so i am totally confused, I am thinking i have to use 2 formulas but I am not exactly sure i tried the formula: Fn = Fg = mg...

how would you find the rate of acceleration when given the force, mass, and the coefficient of friction?? what would the formula(s) be?? i am so confused! HELP!

Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0 If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the original ODE and then solve it analytically or is a numeric solution the only way?

The objective is to find some coefficients by comparing two equations. T_2 \cdot \frac{R_1}{R_1+R_2} + T_1 \cdot \frac{R_2}{R_1+R_2} and T_2 \cdot k_1 + T_1 \cdot k_2 I compare and set k_1 = \frac{R_1}{R_1+R_2} (1) k_2 = \frac{R_2}{R_1+R_2} (2) I expand the...

If f(x) has a period of 2*pi and |f(x)-f(y)| <= c*|x-y|^a where a and c are positive constants, why are are n-th Fourier coefficients <= c*(pi/n)^a ? Help or hints would be appreciated.

Homework Statement For an even function, the Fourier series takes the form ^{\infty}_{n=0}\Sigma A_n cos(\frac{2\pi n x}{\lambda}) where \lambda is the wavelength of the function. In this problem you will see how to find the Fourier coefficients A_n. a.) Prove that A_0 =...

Hello, I'm trying to find a table of basic connection coefficients. My GREAT desire is to find a table that includes the metric, connection coeffs, Riemann tensor, Ricci tensor and Ricci scalar for NORDSTROM's 1913 scalar theory of gravity. Does anyone know an online source of this info...

Hi all, I was reading Lasers and i read something like this: for spontaneous emission, the rate of decay of electrons in high-energy state to low energy state is given by: \frac{dN_2}{dt} = P_{21}N_2 where P21 is equal to the probability of electron to drop from higher energy state...

I'm having some problems recognizing duplication when using the undetermined coefficients method to solve homogeneous type differential equations. http://college.cengage.com/mathematics/larson/calculus_early/3e/shared/chapter15/clc7eap1504.pdf Example 2 on Page 1119, could someone explain...

Homework Statement [PLAIN]http://pokit.org/get/d9a4a8542c2acdfedbb1038292f6817b.jpg Find the coefficients of this function Ck Homework Equations The Attempt at a Solution \begin{align}\Large C_{k}=\frac{1}{T}\cdot \int_{-T/2}^{T/2} f(t)\cdot e^{\frac{-jk2\pi t}{T}}dt=\frac{1}{T}\cdot...

Homework Statement The function f(x)=ln(2−x) is represented as a power series in the form: \sum C_{n}x^{n},n,0,inf Find the first five coefficients in the power series. Basically, this is a problem from my online homework. I did a lot of work to get to my answers, and I feel sort of tired to...

A single-phase ac voltage regulator has a resistive load of R= 10 ohms, and the input voltage is Vs = 240 V, 50 Hz. The delay angle of each of the Thyristors is ɑ = Π/2. Determine: (a) The rms value of the output voltage. (b) The Fourier coefficients of the fundamental, 11th and 13th current...

y''(t) - \frac{2}{t^2}y(t) = 3 - \frac{1}{t^2} In this problem I had to solve two ways: Variation of Parameters and Undetermined Coefficients. I solved it using Variation of Parameters and got the correct answer for the particular solution in the back of the book being y_p(t) = t^2ln|t| +...

hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks

I'm given: y''-y'+\frac{y}{4}=3+e^{\frac{x}{2}} and asked to solve it using undetermined coefficients. Using the auxilary equation y=e^{\lambda t} I got y_{1}=e^{\frac{x}{2}}, y_{1}=xe^{\frac{x}{2}} Now to solve the particular solution, I chose to guess: y_{p}=axe^{\frac{x}{2}}+b and...

Homework Statement For flat spacetime the coefficients of the Lorentz transformation are defined as \alpha^{\nu}_{\mu} = \frac{\partial x^{' \nu}}{\partial x^{\mu}} Whereas the Lorentz transformation is \begin{pmatrix} x_1' \\ x_2' \\ x_3' \\ x_4' \end{pmatrix} = \begin{pmatrix}...

Hello all: I'm using a code for solving partial differential equations that describe transient advection and diffusion. I'm more of a chemistry person, so I'm a bit lost on some of the basics of the calculation method. A general question: As my calculation progresses, I see that...

Homework Statement Hello. I need help with orthogonality of the Fourier series coefficients. I know you can use the dirac delta function, (or the kronecker function) in the orthogonality relationship. I want to try and see the derivation using complex form rather than sines and cosines...

Hello, I'm trying to find the coefficients for the ideal gas specific heat at constant pressure in the form: Cp = a + bT + cT^2 + dT^3 (kJ/kmol.K) I need to find these coefficients for Octane. I have found them online in a slightly different form.. Cp = a + bT + cT^2 + dT^3 + eT^4...

Homework Statement x(t)^double prime-x(t)=tsint Homework Equations The Attempt at a Solution in this case would I start this as x=t(A(2)+A(1))sint or do i also have to use the cos which makes it x=t(A(2)+A(1))sint+t(B(2)+B(1))cost?

Homework Statement determine the particular solution for the differential equation 2x^double prime+x=3t^2 Homework Equations The Attempt at a Solution since F(t)=3t^2 I used At^2+Bt+C and the first derivative is 2A+B plugging back in I get At^2+(4A+B)t+(2B+C)=3t^2 is this...

Homework Statement Find a particular solution y_c to the complex differential equation y'' + 2 y' + 3 y = -1 exp(2 i t) y_c= Using the solution y_c, construct a particular solution y_{1p} to the following differential equation y'' + 2 y' + 3 y = -1 sin(2 t) y_{1p} = Again using...

y_i=A{x_i}^b When I solve for A two different ways I am getting different answers..so somewhere I'm doing something wrong. If someone could point out where I would be grateful :). Using logs: y_i=A{x_i}^b ln(y_i)=ln(A)+b*ln(x_i) ln(y_i)-(ln(A)+b*ln(x_i))=r_i for least squares we want...

Homework Statement A box of textbooks of mass 24.6 kg rests on a loading ramp that makes an angle theta with the horizontal. The coefficient of kinetic friction is 0.23 and the coefficient of static friction is 0.35. A. As the angle theta is increased, find the minimum angle at which the...

solve y''+y'+y=cosx-x2ex y= yc+yp yc: characteristic eq gives r2+r+1=0 using quadratic formula i got r=-1/2+[(sqrt3)/2]i and r=-1/2-[(sqrt3)/2]i so yc=e-x/2(c1cos(sqrt3/2)x+c2sin(sqrt3/2)x but i have no idea of a particular solution that makes any sense. i tried a general...

Homework Statement For the following operator represented in the orthonormal basis {|1>, |2>} \hat{M} = \begin{pmatrix} 2 & i\sqrt{2} \\ -i\sqrt{2 & 2} \end{pmatrix} find the eigenvalues and eigenvectors and express them as a function of |1> and |2> normalized.The Attempt at a Solution I'm...

Homework Statement Calculate the exact value of the sum from minus infinity to infinity of Ck.Homework Equations [SIZE="4"]Ck =...

Hi all, I understand the basic concept of undetermined coefficients, but am a little lost when g(t) in the equation yll+p(t)yl+q(t)y=g(t) is a product of two functions. The specific problem I'm working on is as follows: yll-2yl-3y=-3te-t When I solve for the homogeneous set of solutions I...