Conditions Definition and 978 Threads

Lets ay there is a 0.5 Earth mass and 0.8 Earth radii planet orbiting a Sun like star at the same distance Earth is orbiting its Sun. Its atmospheric pressure would be 0.03 bar. Water boils at 75 degrees F at this pressure. How could an organism living on the surface survive? Another...

True or False. If true explain or prove answer, and if false give an example to show the statement is not always true. 1. If A is a 4x4 matrix and a1+a2=a3+2a4, then A must be singular. 2. If A is row equivalent to both B and C, then A is row equivalent to B+C. My Work: 1. I say it's...

Homework Statement Solve y' = (y^3)(t^2) for the initial condition y(0)=0 and state in which interval in 't' this solution exists. The Attempt at a Solution First I divided both sides by y^3 and then subtracted t^2 from each as well, -t^2 + y'(y^-3) = 0 then solved, (-t^3)/3 +...

Let a,b,c be three 3x1 vectors. Let A be a 3x3 upper triangular matrix which ensures that the 3x1 vectors d,e and f obtained using [d e f]=A[a b c] are orthogonal. a)Express the elements of A in terms of vectors a,b and c. b)what is the condition on a,b and c which allows us to find an...

Homework Statement If utt - uxx= 1-x for 0<x<1, t>0 u(x,0) = x2(1-x) for 0≤x≤1 ut(x,)=0 for 0≤x≤1 ux(x,)=0 u(1,t)=0 find u(1/4,2) Homework Equations The Attempt at a Solution I was thinking to make a judicious change of variables that not only converts the PDE to a homogenous PDE, but also...

Hey! Speaking electrodynamics, I can't seem to get mathematically or even physically convinced that the solution with Dirichlet or Neumann boundary conditions is UNIQUE. Can someone explain it? Thanks.

On the plane z=0 there is a superficial charge distribution such that \sigma is constant. Near to the plane, there is a bar, charged uniform with total charge q. At the extremities the bar has two constraints, so it can't turn. If I want to find the constraints force and the force momentum...

Hello, I'm doing an undergraduate introductory course in quantum mechanics, and I'm having a hard time understanding the interpretation. I've recently learned about the famous "Particle in a box" problem, in which we solve the time-independent schrodinger wave equation to get the energy...

Just posted to the archives is a great new paper from a top experimental team. These are some of the same individuals that performed the now standard citation regarding a Bell test under strict locality conditions. They have now extended their concept to GHZ states, and also close the...

Hi all, Say I am solving a PDE as \frac{\partial y^2}{\partial^2 x}+\frac{\partial y}{\partial x}=f, with the boundary condition y(\pm L)=A. I can understand for the second order differential term, there two boundary conditions are well suited. But what about the first order differential term...

Hi All, I would like to know why in the infinite well problem, after having solved the time independent SE, we are not supposed to equal to zero the x derivative of the spatial part of the wave function at -L and L (2L being the total width). We only have to make it zero at the boundary...

Let Z:= A^T, where T is a countable set and A is a finite set. Under the product topology, Z is a compact metrizable space. (As a special case, notice that Z could be the Cantor set). Given a closed set X \subseteq Z, I'm interested in answering the question, "Does there exist some partition...

Homework Statement When putting a magnet into a solenoid, under what conditions is a current generated? The Attempt at a Solution In order for a current to be generated, the magnet needed to be moving as it passed through the solenoid. This is due to Faraday’s law, which states that an...

Hello, I'm not sure if this should go under the HW/CW section, since it's not really a homework question, just a curiosity about certain kinds of functions. My specific question is this: If M: U→V is injective and dim(U)=dim(V), does that imply that M is surjective (and therefore...

Hi everyone Homework Statement Give is a generall gauge transformation \Phi \rightarrow \Phi ' =\Phi -\frac {\partial \chi}{\partial t} and \vec A \rightarrow \vec A' = \vec A + \nabla \chi first task for now is the following: How do I have to choose Chi in order to fulfill the...

As far as I know, Cherenkov radiation occurs when a charged particle travels through a medium at a greater phase velocity than the speed of light in that medium. Molecules in that medium are polarized and after de-excitation emit radiation. But there are a couple of things about Cherenkov...

As learning laser fundumentals, I've just reviewed the boundary conditions for electromagnetic waves. However, I came back to a point that confused me in the past and want to get it clear now :) One of the boundary conditions, regarding the magnetic fields parallel to the medium-interface...

When we say "pulley is frictionless", do we mean its groove where the string moves or its axle or both?

Hi, I need help to understand this section from my book. Here we are considering drift current Is of PN junction under open-circuit conditions. I don't understand why the drift current Is is indepentent of the value of the depletion layer voltage Vo. I think the voltage create an...

Homework Statement Why are pulleys frictionless and massless in the pulley questions? What would happen if they are not frictionless and not massless? Why are the strings connecting the blocks in pulley questions massless and inextensible? What would happen if they are not massless an not...

How to minimise this function and get initial conditions . I have the answer for initial conditions. ra = min(00237 − 0000175v + 8.693f − 000159y) subjected to 124.53 ≤ v ≤ 167.03 0.025 ≤ f ≤ 0.083 6.2 ≤ y ≤ 14.8 v= 144.2 , f = 0.025, y = 9.5 How to get this?

I'm back with more questions! :approve: I'm wondering what conditions must a manifold satisfy to be able to use Stokes' Theorem. I understand that it must be orientable, but does it have to necessarily be smooth? I tried to see if it was possible to prove Cauchy's Residue Theorem and Cauchy's...

What are the conditions used,While calculating time period of a simple pendulum??

Homework Statement The problem states d^2y/dt^2 +15y= cost4t + 2sin t initial conditions y(0)=y'(0)=0 Homework Equations The Attempt at a Solution All I have is this r^2+15=0 making r(+-)=√15 and making yh= C1cos√15+C2√15 the next part includes solve for...

I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem. d^2y/dt^2 +15y =cos 4t+2 sin t this is what I got so far r^2+15=0 for the homogeneous part r=+-(√15) Yh=C1cos√15+C2sin√15 now is...

Homework Statement I'm trying to find the boundary conditions for the beam shown in the figure. Homework Equations Notation: V= Shear force M= Bending momentThe Attempt at a Solution at x=0 V=R1, M=0 at x=9 V=R3, M=0 In the solution provided at x=9 V=-R2. I don't understand why it's...

Homework Statement I am solving an inclined flow problem, and am stuck. The problem is to find the volumetric flow rate of inclined flow in a square channel. Once I have the velocity profile, I can just integrate over that to get the flow rate. 2. The attempt at a solution Letting the...

So I've been playing with a little N-body code in 3D for gravitational problems and have made an OpenGL visualization to go along with it. I have been generating initial conditions (positions and velocities) using explicit formulas. I was wondering of anyone knew of any resources for getting...

I am looking for strange and interesting planetary circumstances for basing a board game around. This can involve any configuration of planetary bodies and their environments, but must be at least a theoretically possibility in general terms. Perhaps it would be best to illustrate with some...

Hi everyone, I'm attempting to create a computer program to solve the transient 3d heat equation using the Crank Nicolson method. I would like to model the boundaries of my domain as losing heat via convection and radiation due to the temperature difference between the boundary and the air in...

Question 1 The reduced row echelon form of             3 4 17 22 1 2 5 row a b A is equal to             0 0 0 0 0 0 1 2 1 2 0 3 R . (a) What can you say about row 3 of A? Give an example of a possible third row for A. (b) Determine the values of a and b. (c) Determine...

Homework Statement Find the equation of the hyperbola whose transverse axis is x = 3 and goes through: The vertices of 2x^2 + y^2 - 28x + 8y + 108 = 0 and the center of x^2 + y^2 - 6x + 4y + 3 = 0.Homework Equations (x - h)^2/a^2 - (y - k)^2/b^2 = 1The Attempt at a Solution so far I have...

I've attached 2 images above. The first is the problem itself and the answer. It's question 9. So, I tried solving this question using the method of finding the inverse of a n x n matrix by augmenting it with the identity matrix of the same dimensions and then applying row ops in an attempt to...

Homework Statement Find constraints on a,b,c \in \mathbb{R} such that \forall w_1,w_2,w_3 \in \mathbb{C} , (1) x = |w_1|^2(1-c) + a|w_2|^2 + c|w_1+w_3|^2 + |w_3|^2(b-c) \ge 0 and (2) x=0 \Rightarrow w_1=w_2=w_3=0 .Homework Equations The Attempt at a Solution I believe the solution is...

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I have a question about the derivation of the boundary conditions at surfaces of electromagnetic fields. These conditions say, that the tangential component of the electric and the normal component of the magnetic field are continuous at surfaces. Their derivation goes as follows: To derive...

Homework Statement I have question ,i want to solve ODE second order in matlab, but i want to get the answer in terms of constants, because i don't want to give MATLAB initial conditions Is this possible Thank you

Hello! Promising that I will not make other new questions in the next days :smile:, I have a doubt about the meaning of a pair of expressions. Sommerfeld's conditions for an electromagnetic field produced by a finite source bounded by a finite volume are: \lim_{r \to +\infty} r|\mathbf{E}|...

Homework Statement \frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2 Homework Equations None I can think of... The Attempt at a Solution The only thing I even thought to try was turn it into the form: \frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...

Homework Statement problem 4.4 The question: http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/assignments/ps4a.pdf The solution: http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/assignments/sol4a.pdf...

I've been trying to get my head arround this problem for several days now, and while I deemed it relatively simple at first it turns out that I can't figure out the BCs on a conductor, to which we apply a potential U. In the simplified version of the problem, there is a rectangular conductor...

Hi all, I want to ask you a question about the bending moment equation: σ= M * y / I Does this equation have the same form if we assume, -Plasticity instead of elasticity. -Viscoelasticity instead of elasticity. -Nonlinearity instead of linearity. -Anisotropy instead of isotropy...

A = [aij] 1) aij = i +j 2) aij = i^j-1 3) aij = 1 if |i - j| >1 -1 if |i - j| _< 1 I don't even know where to begin. Are i and j compenents of the matrix? Please help me get started

Hi, I shall show (using Fourier transform) that the solution to \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial^2 u(x,t)}{\partial x^2}\\ u(x,0) = f(x) \\ u_t(x,0) = 0 is u(x,t) = (f(x+t) + f(x-t))/2 I got it almost: Taking the Fourier transform in the variable x...

Suppose we have the following IBVP: PDE: u_{t}=α^{2}u_{xx} 0<x<1 0<t<∞ BCs: u(0,t)=0, u_{x}(1,t)=1 0<t<∞ IC: u(x,0)=sin(πx) 0≤x≤1 It appears as though the BCs and the IC do not match. The derivative of temperature with respect to x at position x=1 is a constant 1...

Or at the point at which it starts to rotate... My thinking is that the sliding friction is the only thing that will cause the ball to rotate F = u*N N = mg And moment of inertia I = 2/5*m*r^2 So, when I = 2/5*m*r^2 = u*N = F it will be at the instant of the change over... Am i...

Homework Statement Solve the initial value problem: t(dy/dt)+8y=t^3 where t>0 and y(1)=0 Homework Equations None? The Attempt at a Solution It's a linear equation, so rearranged to dy/dt+8y/t=t^2. Took the integrating factor e^(∫8/tdt)=t^8 and multiplied through...

Sorry for the poorly-worded title. I help tutor kids with pre-calculus, and they're working inverse functions now. They use the "horizontal line test" to see if a function will have an inverse or not by seeing visually if it's one-to-one. I was thinking about what that might imply. If a...

I am familiar with standard distance-time models for paths of projectiles in perfect conditions, ie, where the curvature doesn't play a role, and where gravity is constant no matter the height. My question is what if you launch a projectile so high that the curvature of Earth plays a role, and...

The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...