Derive Definition and 620 Threads

Homework Statement Starting from: vg=vp+k(dvp/dk) show that the group velocity can also be expressed by vg=vp-λ(dvp/dλ). Homework Equations I'm told that vg=vp+k(dvp/dk) with vg=group velocity and vp=phase velocity. I also know that k=(2π)/λ and ω=2πf. The Attempt at a Solution I...

Hi guys, I was reading the derivation of ficticious force due to moving frame of reference however i don't understand how they did it.There wasn't detail explanation for slow learners like me so i was wondering does anyone know where i can read up on this or give me some clue where i can start...

i recently started my calculus III course but i was stuck with the derivative part when i derive a real number to the power x ( like 2^x) and also when deriving x^x. does anybody have an idea or a link in which these kinds of derivatives can be solved. thanks for ur help

Homework Statement Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity: (dCv/dV)T = T(d2P/dT2)V Homework Equations The Attempt at a Solution I have no idea, please help

For some reason I have been extremely curious of how Newton derived his mathematical law for gravitation. You know F= \frac{GMm}{r^2} So the first thing I did before i posted this was search Google and I foundhttp://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml" . It...

These 2 questions are confusing me, I have some idea about what to do, can someone help? Question 1 Homework Statement Consider a circular track with a radius of 200 meters, suppose it takes 2 minutes to run from her starting point to the opposite side of the track. What is the magnitude...

I am currently studying a great text Elementary Differential Equations and Boundary Valued Problems 9th edition; and we have come to chapter 5 and are studying Ordinary Points, Singular Points, and Irregular Points. (get the point?) Anyway, I did see these mentioned,, this...

Homework Statement Derive sin^2 + cos^2 = 1 Homework Equations Use cos 0 =1, cos (x+y) = cos x cos y - sin x sin y Earlier someone posted this same question, but I still don't understand it so please help

Can someone please explain the steps to derive this? I've seen it everywhere, but the explanation is never given. My confusion arises from the second line. In EVERY math book I've ever picked up, whenever you take a derivative, it is ALWAYS with respective to something, i.e y w.r.t x, or...

If the covariance matrix \mathbf{\Sigma} of the multivariate normal distribution is invertible one can derive the density function: f(x_1,...,x_n) = f(\mathbf{x}) =...

(gamma)ma=F-[F.(beta)]beta How derive this?

Homework Statement how to derive this equation? and Homework Equations The Attempt at a Solution I try derive it that to cut out high degree part such as delta_R1*delta_R2 because my teacher told that is very small and near to zero. but I can't made it to that...

I've seen one derivation on Feynman Lectures on Physics, but the derivation is not really rigorous(he took a very special case for the derivation),I googled about the topic and couldn't find a satisfactory one. So can anybody give me a rigorous one? Thanks in advance

Homework Statement So I made a spring launcher that will fire marbles. I need to derive a general formula for finding range for any given angle and x value.Homework Equations 1) v22=v12+2ad 2) Ek=Es 3) 1/2mv2=1/2kx2 4) d=v*t This projectile was shot from 1.1m off of the ground. The Attempt at...

Hello everyone, During the last few days I've been working to solve a "small" problem I hope someone here might be better at than I am. I'm writing a function that returns the state vectors of an orbiting body of neglible mass based on the orbital elements semimajor axis, semiminor axis...

Homework Statement Derive the following inequality. Homework Equations x^{2}+xy+y^{2} \geq 0 The Attempt at a Solution I don't know how to get started. How do you derive inequalities? I'm not looking for the answer, just general tips.

(\textbf{q}\bullet\nabla)(\textbf{p}\bullet\nabla)\frac{1}{r} = -(\textbf{p}\bullet\textbf{q})\frac{1}{r^{3}} + 3(\textbf{p}\bullet\textbf{r})(\textbf{q}\bullet\textbf{r})\frac{1}{r^{5}} r is distance between field point and dipole source, \textbf{p} is dipole moment, and I believe \textbf{q}...

How may I derive y=cos^3(sinx)? I thought simply just y=3cos(sinx)^2(cosx)... Answer given is -3cosxsin(sinx)cos^2(sinx) but no idea how to get to that.

Homework Statement i need to derive the ideal gas law Homework Equations this is the equation to end with. PV=NkT The Attempt at a Solution I am not entirely sure where to start with this derivation. I believe Newton laws. where your going to have Fx= Px/t anyone...

Initial Velocity of Projectile given: - let theta be: B -equation for: (E1)horizontal component is x = vxt; where vx= v0cosB (E2)vertical component is y= y0 +vyt - (1/2)gt(squared); where vy = v0sinB using these components an equation of initial velocity{v0} =...

Can general relativity derive from superstring theory?

How do you derive this (E=v/d)?

Investigating how a car bounces with the framework of an idealized model. Let the chassis be a rigid, square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K,K,K and k < K (the faulty one). The springs are confined so they stretch and compress...

I've been looking everywhere for a tutorial or lesson on Parametric equations and can't find one that shows how to derive the actual equations. Either they show how to eliminate the parameter or sketch the graph. Let's say you had a function like y = x^2 + x - 3 What would you do to find the...

So I know that sine of an angle is the side opposite of the angle in a right triangle divided by the hypotenuse. What i want to know is: if i have an angle in a right triangle how do i find the sides of the triangle so i can find Sine. I spent my study hall trying to figure it out and this is...

Is it possible to derive Heisenberg's Uncertainty principle just using Schrodinger Equation? If yes, is there any source that you can refer me to?

Homework Statement Derive the equations for v0 and R, and show how you made your prediction. Homework Equations d = v0t +1/2at^2 The Attempt at a Solution The acceleration was zero, so I rewrote the equation: R(range) = v0t but then they substituted t with\sqrt{\frac{2Y}{g}}...

3. Beginning from Newton’s rule for the gravitational force = -GMm/r^2 derive an expression for the potential energy of a particle of mass m above the surface of the earth, and show that it can be written as: U(r) = -g0 RE/r where r is the distance from the centre of the earth, RE is the...

Homework Statement a. The first part of this problem was to derive the escape speed (Vesc) for a star of mass M and radius R. b. The second part is where I am having trouble. It says to equate the Vesc calculated above and derive a formula for Planck length in terms of c, G, and h_bar...

Any hints on how to derive the glass viscosity? n=n(0)exp(Q/RT)?

Homework Statement Approximate an infinite field of charge as a sheet of infinitely long charged wires each with charge dQ = λL . Use the formula for the electric field of a wire in the limit as L goes to infinity to derive the formula for an infinite sheet of charge dencity η. You need to...

Homework Statement x1,x2) are the components of a 2 dimensional vector r when referred to cartesian axes along the directions i,j. derive the relations x1'= cosΘ x1+sinΘ x2 x2'=-sinΘ x1+cosΘ x2 for the components (x1',x2') or r referred to new axes i',j' obtained by a rotation of the axes...

Homework Statement For temperatures T >> T_C (critical temperature) derive the heat capacity at constant pressure C_P from van der Waals equation. Homework Equations Critical temperature: T_C = \frac{2N(V - Nb)^2}{kV^2} T_C is derived from the fact that it exist at the point in which...

Homework Statement the fahrenheit temp scale is defined to that ice melts at 32 F and water boils at 212 F. Derive formulas for converting fahrenheit to celsius and back. Homework Equations c=5/9(f-32) The Attempt at a Solution ok so i figured that 212-32= 180 and 100-0=100 so...

Homework Statement Derive the compton equation. Homework Equations \lambda` - \lambda = h/ mc (1 - cos\theta) E = hf = hc/\lambda The Attempt at a Solution Okay, I'm sorry this is so long, I'll try and make it as concise as it is possible for a whole blather of random crap to...

Sorry me again THE CRC tables define the above integral as using sqrt(x^2-a^2) let t(x) = sqrt(x^2 - a^2) integral = 1/2( x T(x) - a^2 log( x + T(x)) HOW do they arrive at this. Thanks

Homework Statement This is from Advanced Physics by Adams and Allday, section 9.11, question 3. I am posting hints for the solution because it took me so painfully long to understand what the text and the question were and weren't saying and hence to find the necessary extra information...

[Solved] Centripetal Acceleration Homework Statement Derive the magnitude and direction of the linear acceleration at the tip of the stick, ignore the effect of gravity. Homework Equations r = length of stick a = dv/dt The Attempt at a Solution I first find the x and y components...

Homework Statement Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if: f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ] I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when...

Homework Statement A planet with mass m is orbiting about the Sun (mass m(s)) with elliptical orbit such that the maximum and minimum distance is r1 and r2 respectively. What is its angular momentum, L, of the planet relative to the centre of the Sun? Homework Equations...

Homework Statement A planet of mass m orbiting the Sun(mass=m_s along an elliptical orbit, with aphelion r1 and perihelion r2. Find the angular momentum of the planet relative to the centre of the Sun. Homework Equations Angular momentum, M=m(R\times v)=mvR sin\theta Distance from Sun...

Homework Statement Derive the Law of Conservation of Mechanical Energy starting from the Work-Energy Theorem. State any assumptions. Homework Equations I'm not really sure where to start with this. Basically how to end up with the equation 0=\DeltaU+\DeltaK The Attempt at a Solution

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

Homework Statement If you have a function f_n(x), how do you get the equivalent representation <x|f>? Homework Equations I have a system with a given Hamiltonian (not in matrix-form), from which I derived the specter of energy eigenvalues E_n, and the corresponding energy...

How do I derive this equation?!? HELP! I started with the equation: y=yinitial + (vinitialsintheta)t -1/2gt^2 I plugged in t=x/(vinitialcostheta) to get: y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))] Using derivatives, how do I get from this equation: y=yinitial...

Given the equations V2x= V1x+ax\Deltat and \DeltaX= V1x\Deltat+ 1/2ax\Deltat2, i need to derive the equation V2x2=V1x2+2ax\Deltat. please help me!

Homework Statement A wire OA connects the collar A and a reel located at O as shown in the picture. Knowing that the collar moves to the right at a constant speed v0, determine θ'' (the 2nd-order-derivative of θ) in term of v0, b and θ. http://www.freeimagehosting.net/uploads/3cad8b54c6.jpg...

Starting with the equation of motion -kx = ma , it is said that integrating this with respect to x gives the equation for conservation of mechanical energy. Only problem is i don't see how to integrate the right hand side with respect to x...

How to derive equillibrium constant (K) of reaction with respect to water eq. constant (KH2O) ? Reactions H+ + HCO3- ----------> H2CO3 H+ + CO3-2 -----------> HCO3- Fe2+...

1. The problem statement Derive the sine power series without using Taylor's formula.