Initial Definition and 1000 Threads

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...

Hİ. How can we sure that the initial conditions , say, for a second-order linear equation must be unique which is also the uniqueness of the solution.

Hey there, I have modeled a propagating wave in a 1D dispersive media, in which square and cubic nonlinear terms are present. u′′=au3+bu2+cu the propagating pulse starts to steepen with time which is the effect of nonlinearity, but there is an effect which I can't understand. so...

Homework Statement Imagine that a bullet is shot vertically into the air with an initial speed of 9800 m/s. If we ignore air friction, how high will it go? vi = 9800 m/s h = ? Homework Equations v2 = vi2 + 2aΔy Ki = Ui --> 1/2mv2 = mgh F = (Gm1m2)/r The Attempt at a...

It's not homework training problems...I have the answers but I get wrong ans. Homework Statement problem 1 What was the initial speed of a meteorite of mass 1 kg if a total of 18 MJ of thermal and other forms of energy were produced during its fall through the atmosphere of a planet and its...

In a new Olympic event athletes run as fast as they can, jump onto a sled, ride it down a hill and compress a spring as far as they possibly can. (who thinks of these any ways) a. Consider a 55.0 kg athlete that makes it to a top speed of 12.5 m/s before jumping onto a 15.0 kg sled. What is...

I have this equation u0(x) = a0x2(1-x)2 for 0≤ x ≤ 1 = 0 for x>1 i have to investigate how will a solitary initial state such as the one above deform as time goes on. I know it will not deform if c is constant. when they say I must do this by a well-lnown method and produce video...

Hi everyone! I am doing a simulation of threaded connection in ANSYS workbench and have some problem. In this 2D model, the initial make-up is modeled by setting an "initial overlap" (shown in figure 1). This is how I did: - The initial contact between pin and box as "frictional" with...

Homework Statement Here is the question I'm trying to answer: A tennis player hits a 1.45 kg tennis ball with a racket of mass 2.5 kg. If he hits the ball with a velocity of 7.5 m/s and then stops, what impulse did he imply on the ball? What is the ball’s velocity? Homework Equations...

Homework Statement Find the initial wavelength of a photon that loses half its energy when it Compton-scatters from an electron and emerges at 90∘ to its initial direction of motion. The Attempt at a Solution Ei = Ef +KE Ei = 0.5Ei + KE Using compton's formula for scattering...

Homework Statement An 1.94 m tall basketball player wants to make a basket from a distance d = 19.8 m. If he shoots the ball at θ = 58.7° angle, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basketball hoop...

So, I had initially kept the values of X as 0.0D0 for all my 14 variables and it wouldn't populate any results. This was mainly done based on the guide that I was referring to. On contacting my tutor, he placed the following values instead? X(1) = 0.0D-01 X(2) = 0.0D-02...

Hey! :o I have to solve the following initial and boundary value problem: $$u_t=u_{xx}, 0<x<L, t>0 (1)$$ $$u_x(0,t)=u_x(L,t)=0, t>0$$ $$u(x,0)=H(x - \frac{L}{2} ), 0<x<L, \text{ where } H(x)=1 \text{ for } x>0 \text{ and } H(x)=0 \text{ for } x<0$$ I have done the following: Using the method...

Homework Statement The problem is from Walter Gautschi - Numerical Analysis, exercise 5.1. Consider the initial value problem \frac{dy}{dx}=\kappa(y+y^3), 0\leq x\leq1; y(0)=s where \kappa > 0 (in fact, \kappa >> 1) and s > 0. Under what conditions on s does the solution y(x) =...

Why is the initial current through the inductor 20A? Surely the current splits at the junctions?

Hi every one Homework Statement If (R) is to be the horizontal range of a projectile and (h) its maximum height prove that the initial velocity is: [tex] \sqrt{(2g(h+\frac{R^2}{16h}))} [\tex] Homework Equations [tex]R=\frac{v_0^2 sin(2\theta)}{g}[\tex] [tex]h=\frac{v_0^2...

A ball is thrown from a cliff. The path of the ball modeled by the equation h = -5t^2+ 5t + 210, where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff? Not really sure how to do this problem. I know that one of...

Homework Statement I managed to work this problem all the way through, but I am in no way certain of my answer. I'd greatly appreciate any insight! Find the solution of the initial value problem. y'''+4y'=x, y(0)=y'(0)=0, y''(0)=1 Homework Equations Just for clarification...

Hi, I've attached a couple questions just because these are the type of questions I've had some difficulty solving since I don't recall addressing anything too similar too similar in the past (i.e., changing velocity and determining how the amplitude varies because of this). I know to go from...

I've been trying to tackle this question for a while now, but I'm afraid it's not going anywhere without some outside help. So let's say we have some body falling towards a planet without any atmosphere, and let's assume that the initial velocity is not equal to zero. Given these conditions I'm...

Homework Statement Tom decided to attempt to jump a 200m wide river on rocket skates. He built a 60m long ramp with an angle of 30° to the horizontal and plans to land on a mattress at ground level. Determine the launch speed necessary for Tom to be successful. Homework Equations I read...

What would be the practical application of reducing the initial time step in a FE analysis. By Initial, I mean - the commercial software always calculates stable timestep based on geometry and material properties. There is always a provision given to use a lesser time step value at start of the...

given this equation x' = f(x)= square root(1-x^2) x(2) = 1 I hae to show that teh solution is not unique my work: i tried to find the interval in which f(x) is defined, i said: 1-x^2 ≥ 0 (because of the sqrt) -x^2 ≥ -1 x^2≤ 1 x≤ ±1 my problem is if i take a number < 1 and substitute it on f(x)...

Homework Statement a stone is thrown vertically downward from the top of 40 m tall building with an initial speed of 1 after 2s the stone will have traveled a distance of? Homework Equations x=vt+0.5at^2 vf=vi+at The Attempt at a Solution 1(2)+0.5(-9.8)(2)^2=-17.6 the answer i...

solve the initial value problem: x'=x^3 x(1)=1 my work dx/x^3 =dt then I integrated wrt t and obtained x^(-2) = t + c(c0nstant) where then this is 1/x^2 =t+c 1/x = square root of (t+c) then x= 1/sqrt(t+c) now when i apply the Initial value problem i get c = 0 and that is incorrect. where am...

Homework Statement Two capacitors, C1 = 4μF and C2 = 9μF, are connected in series with a 30 V battery. The battery is removed and the plates of like sign are connected. Find the initial and final energies for each capacitor. Homework Equations Q=C*V U=q^2/2C Ceq = ∑Ci ( don't know...

Homework Statement 4y" + 4y' + 5y = 0 y(0) = 3 y'(0) = 1 Homework Equations yh = e^ax(c1cosbx + c2sinbx) The Attempt at a Solution For the roots I got -1/2 + i and -1/2 - i so my a = -1/2 and b = 1 then I have to differentiate yh = e^(-1/2x)[c1cosx + c2sinx] this is where I get this...

Hi :) I'm reading a didactic paper and the author defined the initial state ket as |\Phi_{in}> = {\int}dq\phi_{in}(q)|q> where q is a coordinate and \phi_{in}(q) = <q|\Phi_{in}> = exp\left[\frac{-q^{2}}{4\Delta^{2}}\right] I don't know if I'm missing something but isn't this definition a...

How to solve this question. Please explain step by step.

Homework Statement In figure shown, pulleys are ideal m1 > 2 m2. Initially the system is in equilibrium and string connecting m2 to rigid support below is cut. Find the initial acceleration of m2? Homework Equations The Attempt at a Solution In equilibrium, 2T1 = T2 For...

Homework Statement Consider the RL circuit shown in the figure. Assume that the current ##i(t)## has reached a steady state with the switch at position ##A##. At time ##t = 0##, the switch is moved from position ##A## to position ##B##. http://imgur.com/dRIOrp0 If I use the image button...

In atomic bomb there are two hemispheres of fission material (Uranium or Plutonium), they are joined by means of conventional chemical explosives, the necessary critical mass is reached and the atomic bomb explodes, everybody knows this: But is this condition enough? Indeed, the initial...

I'm getting pretty lost with how initial data works in general relativity. Assuming the energy momentum tensor is known (coupled with the metric somehow), what is initial data required to determine the metric at all later times?

Homework Statement I have been trying to follow a solution to a problem I had but do not quite understand the whole thing. I wondered if anybody could clear it up for me. Let a_0 be the initial value of 'a' for which the transition from one type of behaviour to another occurs. The...

I thought there was a difference, but I'm being told now that the time independent wave function is the wave function at t=0

Laplace transform initial value problem--need help! Looking at the solutions to these initial value problems, I am very confused as to how the highlighted steps are derived (both use heaviside step functions). I know the goal is to get the fractions in a familiar form so that one can look them...

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. For my phase diagram all the arrows are pointing up so the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above differential equation with...

Burgers Equation Question -- cannot satisfy initial conditions Homework Statement Use characteristics to solve u_t+uu_x=0 on half line x≥0 with u(x,0)=x^2 Homework Equations NA The Attempt at a Solution I think I have an issue with the initial condition. So solving via...

AP Physics student here, I'm working on a problem that takes into account air resistance, where something is thrown up at initial velocity v_0, and the drag force is proportional to the velocity, so, \vec{F_{drag}}=-k\vec{v}. Using Newtons second law and making up positive, down negative, you...

Homework Statement Determine the minimum initial velocity V0 and the corresponding angle theta at which the ball must be kicked in order for it to just cross over the 3 m fence. Given: Horizontal distance=6m vertical distance=3m Homework Equations equation 1: Vy2=(V0)2+2a(y-y0)...

Homework Statement Solve the initial value problem: y+(3x-xy+2)dy/dx = 0 , y(1)=1 I couldn't separate with y as a dependent variable, so I made x the dependent variable and I get this: dx/dy= x(1-2/y)-(2/y), in linear standard form: dx/dy+(3/y - 1)x = -2/y. Homework Equations...

Homework Statement One mole of an ideal diatomic gas with C_{v} = \frac{5R}{2} occupies a volume Vi = 2.14 m^{3} at a pressure P_{i}=1 atm. The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process, it is found that the rms speed of the gas...

Hello! :) I have a question.. Suppose that we have a finite automaton $A$(deterministic or not) and $L(A)$ the language that it accepts.It interest us to recognize the complement language $L'=(\Sigma^{*}-L(A))$.So,we reverse the states of A as followed:we make the accepting state non-accepting...

Homework Statement Hello, A dipole moment is placed in a uniform electric field oriented along an unknown direction. The maximum torque applied to the dipole is equal to 0.1 N.m. When the dipole reaches equilibrium its potential energy is equal to -0.2 J. What was the initial angle between the...

Homework Statement dy/dx =4yx^3-y y(1)=-3 dy/y = (4x^3-1)dx ln(y) = x^4-x+C y = e^(x^4-x+C) But an answer source says that after the integration I get ln(y) = x^4 - x + ln(C) so then.. ln(y/c) = x^4 - x y = Ce^(x^4 - x) which makes it much easier to solve for the constant given...

Homework Statement A ball thrown vertically from ground level is caught 3.0 s later by a person on a balcony which is 14 m above the ground. Determine the initial speed of the ball. t = 3.0 s, d = 14 m, Vi = ? Homework Equations d = Vi.t + 1/2 a.t^2 The Attempt at a Solution I...

Ok, I am a bit stuck on a homework problem. I know the following: Initial speed: 25 m/s Distance: 49.85 m Initial height: 30 m And that is it. I know that one possible initial trajectory is 70 degrees, but I need to find the other, and that is where I am having a problem. Of the equations that...

1. Problem a basketball player is standing 9.5m from the basket which is at a height of 3.1m. She throws the ball from an initial height of 2.0m at an angle of 35 degrees above horizontal. The ball goes straight through the basket. Find v initial 2. Equations Any range / Kinematic equations...

I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.)...

Given a PDE of order 1 and another of order 2, you could show me what is, or which are, all possible initial conditions? For an ODE of order 2, for example, the initial condition is simple, is (t₀, y₀, y'₀). However, for a PDE, I think that there is various way to specify the initial condition...