Initial Definition and 1000 Threads

Eq u'(x)+p(x)u=f(x) with initial condition u(0)=0 It's homogenous solution is u_h=Ce^{-\int^x_0 p(s)ds} Complete solution u(x)=e^{-\int^x_0 p(s)ds}\int^x_0f(s)e^{\int^s_0 p(z)dz}ds=\int^x_0 f(s)g(x,s)ds where g(x,s)=e^{-\int^{x}_s p(\xi)d \xi } I didn't see that last...

Hi, I was wondering if someone could point me to a textbook or easy to read paper (or website) that briefly describes/proves the differences here. What I mean is if I do classical (continuous energies) statistical mechanics where my initial state is a volume (greater than or equal to h-bar)...

Homework Statement A spherical billiard ball radius a and mass M is sitting on a flat surface. The coefficient of friction between the ball and table is u. The moment of inertia for the billiard ball is 2Ma^2/5. The ball is given a sharp horizontal hit at the centre and it starts moving with...

Homework Statement Show that R_{00}= -\frac{1}{2}g^{\alpha\beta}g_{\alpha\beta,00}+ M_{00}, where M can be expressed solely in terms of the initial data, which is the metric tensor and its first derivatives. Homework Equations R_{ab}= R^c_{acb}= \Gamma^a_{bd,c}- \Gamma^a_{bc,d} in...

Can someone the following steps of this solution for me? http://imageshack.us/photo/my-images/828/80685231.jpg/ Mainly how they got their initial conditions? The 7.30 equation is just h[n-m] = bm which doesn't help me much. For our problem, I know that n=3 and m =1 since the LHS...

Homework Statement We know that y = Aex is the solution to the initial value problem dy/dx = y; y(0) = A. This can be shown by solving the equation directly. The goal of this problem is to reach the same conclusion using power series. Method: Let y be a solution to the initial value...

I need help to solve this problem: The initial mass function (IMF) of main-sequence stars, n(M) follows a shape called the Salpeter function,which is described by n(M)=kM^-2.35, where k is a normalising constant and M is the stellar mass in solar masses. The IMF is similar in some sense to a...

Homework Statement I need to find Vi, knowing the following: Δt=6/Vi cos40 Viy=Vi sin40 Δy=4m ay=-g = -9.8m/s^2Homework Equations Quadratic: x= [-b +/- √(b^2-4ac)]/2a Kinematic equation to be used: Δy=ViyΔt + 1/2ayΔt^2The Attempt at a Solution Δy=ViyΔt + 1/2ayΔt^2 4=(Vi sin40)(6/Vi...

How to find the initial velocity required for a projectile to be launched at an angle theta, with a distance 'd' and height 'h'. An expression is required. I am unable to find one using all three. Thanks in advance.

Homework Statement Calculate reservoir pore volume in field units and initial gas in place for a formation with total bulk volume of 1E8 m^3. A sample of the reservoir gas mixture has 15 moles of CH4 (Tc = 191K),Pc = 46.1bar), 2 Moles C2H6 (Tc =306K, Pc = 48.8 bar) 3 Moles C3H8 (Tc =...

[b]1. A fixed amount of gas initially at 100 K and pressure P1 is expanded from 1 L to 100 L in a piston. The temperature, T2, of the gas at this point is 50 K. The piston is then locked at constant volume V2=100 L and half the gas is pumped out at a constant temperature of T2 . The observed...

Homework Statement An ice-water mixture has a mass of 180g and is contained in a 100g aluminum calorimeter When 35g of steam at 100 degree Celsius is condensed in the water, the temperature rises to 50 degree Celsius. How much ice was in the container initially? The heat capacity of water is...

HI all There is smth I don't understand in building initial data for BH The equations everybody uses uses spacetime or timelike hypersurfaces but for example horizon is a null surface!

Homework Statement A 10 g ball going at a speed of 5 m/s is kicked, and flies off at an angle of 35° at 25 m/s. What was the force of kick? Known: m = 0.0010 kg vi = 5 m/s θ = 35° vf = 25 m/s Homework Equations mvi = mvf F = ma The Attempt at a Solution Would this count as an...

So, let's assume the switch has been closed for a long time. The capacitor is charged to 12V, and the coil acts like a short-circuit. Immediately after opening the switch, is it right to say the Voltage in the coil is 12V? My notes specify something along the lines of: the conditions at time...

Is there any way to mathematically derive functions that satisfy a given set of initial conditions? I know this sounds very general, but say for: f(1)-f(0)=0 and f'(1)=1 I've resolved myself to guessing and checking. I've found a function for the opposite: e*t-exp(t) -- ([e*1 -...

This problem has been bothering me for a while now, hope you can help me. Let's say that the initial velocity of an object, with mass of m is 0 and the initial position is s0 and the force acting on the object is defined as F(s), how do i find the s(t), where t is time. If it's any help, then...

Hi everyone, I am building a 2D geometry and specify the corresponding initial temperature (non-uniform in the domain) with the aid of MATLAB (liveLink Matlab). The geometry creating is almost finished, while the initial temperature problem puzzles me a lot. The initial temperature at...

Given: Mass= 5 kg Vo= 40 m/s Vf=50 m/s s=150 m Ho=0 Hf=50.2 m g=9.8 m/s/s friction=6.26 N θ=30° *You will probably not use all of these values* What percent of initial total mechanical energy is lost during the round trip? (a block (with mass m) going up an inclined plane, and...

Hello everybody, I was wondering whether someone has more information on the influence of inconsistant initial conditions on solving a system of ODE's with periodic solutions using a time marching method like a 4th order Runge-Kutta scheme. The phenomenon I am studying is described by a...

Homework Statement 3y'' -y' + (x+1)y = 1 y(0) = y'(0) = 0 Homework Equations Not sure, that's the issue The Attempt at a Solution I can't quite get this one using the methods I'm familiar with, and I can't guess a particular solution to neither the equation nor the...

Homework Statement A block with mass m = 7.4 kg slides down an inclined plane of slope angle 43.8 ° with a constant velocity. It is then projected up the same plane with an initial speed 3.10 m/s. How far up the incline will the block move before coming to rest? The attempt at a...

Hi All, It's been a looong time since I've had to use/apply basic physics but I'm hoping I've come to the right place for help. I am trying to help my brother-in-law with a speeding charge. First question The police allege he reached 100km/h within 38m of a corner. The first...

So the question I'm asking about is actually from my analytical mechanics class, but I think my question is really more of a gen. physics question. Basically, in this question we have a cannon ball, diameter(EDIT:but not mass!), fired with a given muzzle velocity, and we are given the cannon...

Hi I need to find the horizontal distance traveled by an aircraft just after take off to a vertical height of 10.7m. The rate of climb is 1920m/min. I'm not really sure how to approch this question. I think simply it would look like a right angles triangle, I would need an initial velocity...

Question: Find y as a function of x: x^2 y'' + 8 x y' - 18 y = x^8 y(1)=3, y'(1)=2 Attempted solution: I found the general equation to be Ax^(-9)+Bx^2+Cx^8. However when I try to solve the initial value problem for this equation I have 3 unknowns.

Homework Statement Consider the PDE xu_x + y u_y = 4 u, -\infty < x < \infty, -\infty < y < \infty. Find an explicit solution that satisfies u = 1 on the ellipse 4x^2 + y^2 = 1. Homework Equations The Attempt at a Solution The characteristic curves are x(t,s) = f_1(s) e^t...

The questions arises because I want to use the solution of one PDE as initial condition to solve another. Then using NDSolve, the first solution is given by InterpolatingFunction. I tried, it takes the whole afternoon, almost kills my computer but still not giving any result. Another computer...

Homework Statement A 20.00kg curling stone is released at the hog line and moves 28.35m [W] to sit on the button and score a point. If the coefficient of kinetic friction between the stone and the ice is 0.0020000, what was the initial speed of the stone ? So we know: m=20.00kg...

The problem: dx(1-y^2)^1/2=dy(1-x^2)^1/2 y(0)=3^(1/2)/2 My attempt: I separated the variables and integrated, and came up with sin^-1(x)+c=sin^-1(y) This is where i am stuck. any suggestions? did I run astray anywhere?

Homework Statement I have found the general solution to a second order pde to be U(x,t) = f(3x + t) + g(-x + t) where f and g are arbitrary functions I have initial conditions U(x,0) = sin(x) Du/dt (x,0) = cos (2x) The Attempt at a Solution I have found that U(x,0) = f(3x) +...

Homework Statement In this problem, we will solve the initial value inhomogeneous differential equation in two steps. y''+4y=2x*e^(3x) y(0)=0 y'(0)=0 1.) First determine yp the particular solution to the differential equation. 2.) Next determine y=yc+yp the complete solution...

Homework Statement I have a PDE for which i have found the general solution to be u(x,y) = f1(3x + t) + f2(-x + t) where f1 and f2 are arbitrary functions. I have initial conditions u(x,0) = sin (x) and partial derivative du/dt (x,0) = cos (2x)Homework Equations u(x,y) = f1(3x + t) + f2(-x +...

Homework Statement A student is determined to test the law of gravity for himself. He steps off a skyscraper 320m high, stopwatch in hand, and starts his free fall. Five seconds later, superman arrives at the scene and dives off the roof to save the student. What must superman's initial...

I'm given the following DE and initial conditions: y''=2yy' y(0)=0, y'(0)=1 I started by doing a reduction of order like so: w=y', w'=y'', \int w=y=\frac{w^{2}}{2}+c which then gave me this: w'=2w(\frac{w^{2}}{2}+c) w'=w^{3}+2wc Now I'm stuck on where to go from here. I can't use any of the...

Homework Statement An arrow is shot at an angle of θ=45* above the horizontal. The arrow hits a tree a horizontal distance D=220m away, at the same height above the ground as it was shot. Use g=9.8m/s^2 for the magnitude of the acceleration due to gravity. Find t, the time that the arrow...

Hi all Another question (sorry) Water vapour in the air will phase shift back to liquid when it reaches its Dew Point temp (Partial Pressure = the Saturated Vapour Pressure), OK I have this. For this phase shift I assume that there are Condensation Nuclei and these nuclei are at a lower...

According to the usual way of applying determinism in physics:- If we know all the intitial conditions of a closed system at time t0, we can fully specify the the system at a time t1>t0. This seems natural and obvious within classical physics, but is it really true? I have never heard of a...

Homework Statement A baseball player throws a ball a distance of 250 ft. If the ball is released at an angle of 45°with the horizontal, find its initial speed. Homework Equations The Attempt at a Solution I don't know where to begin. All i know is that speed is the norm of...

Homework Statement A block is given a push up an inclined plane with an initial velocity. At what time will the speed of the block be equal to the initial velocity again? No varialbes are given. Homework Equations v= v(initial) + at The Attempt at a Solution The final...

Homework Statement A woman running at constant velocity speeds up and accelerates uniformly to the west by running 253 m west in 6.12 s. ff she ends up getting up to a velocity of 5.05 m/s w, how fast was she going originally? If she had run the same disance in 5.50 s, what would her average...

Homework Statement A ball is shot from a slingshot and clears a 10 meter fence 130 meters from the point of being flung and lands 10 meters behind the fence. What is the initial velocity of the ball? Assume the ball was caught at the same level it was kicked (delta Y=0). Homework...

Homework Statement A 50.0kg skier starts at A with an unknown initial velocity. The skier then goes over a hill (point B) which is 4.00m above point A. At point B (top of the hill), the skier experiences a Force normal 5/6 of his/her weight. The hill has a radius of 14.6m. What is the...

Because of the kinetic energy and frames of reference thread: https://www.physicsforums.com/showthread.php?t=534883 I was wondering how to show that a change from potential to kinetic energy in a closed system is independent of the (inertial) frame of reference. I think the math below...

I'm trying to help a friend with a physics problem. I've been helping her figure a few out(I always make sure she solves them and understands how she did) but we've hit one that's gotten us both stumped, so I'd appreciate a bit of assistance. The problem is basically, a Diver dives off a...

Why is it that you are able to have 1 initial value problem with 2 solutions, but not 2 initial value problems with 1 solution for an ODE? Is there a theorem that states this?

Homework Statement A rock is thrown downward from an unknown height above the ground with an initial speed of 27 m/s. It strikes the ground 7.1 s later. Determine the initial height of the rock above the ground. The acceleration of gravity is 9.8 m/s2. Answer in units of m. Homework...

Homework Statement See image Homework EquationsSee image The Attempt at a Solution I have tried, but I honestly have no Idea how to start this problem.

Homework Statement A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 0.77 s after leaving the dock has a magnitude of 7.4 m. What is the car's speed at the instant it drives off the edge of the dock? @t = .77s displacement is...

Homework Statement Material ejected to a height of 2.00 x 10^5m. Acceleration of gravity is 1.80 m/s^2, find initial velocity Homework Equations v (zero) = v - at. The Attempt at a Solution Seems as though I am missing something since I don't have time or velocity, yet I have...