What is Initial: Definition and 1000 Discussions

In a written or published work, an initial or drop cap is a letter at the beginning of a word, a chapter, or a paragraph that is larger than the rest of the text. The word is derived from the Latin initialis, which means standing at the beginning. An initial is often several lines in height and in older boscene are known as "inhabited" initials. Certain important initials, such as the Beatus initial or "B" of Beatus vir... at the opening of Psalm 1 at the start of a vulgate Latin. These specific initials, in an illuminated manuscript, were also called initiumsIn the present, the word initial commonly refers to the first letter of any word or name, the latter normally capitalized in English usage and is generally that of a first given name or a middle one or ones.

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  1. M

    Solving Homogenous Eq. with Initial Conditions: u(x)=\int^x_0 f(s)g(x,s)ds

    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...
  2. maverick_starstrider

    Classical Stat Mech with Uncertain Initial Conditions vs. Quantum

    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)...
  3. E

    Rolling motion of sphere (weird initial condition?)

    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...
  4. P

    How Can R_{00} Be Expressed Using Initial Data in General Relativity?

    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...
  5. C

    How do you find initial values for linear discrete time systems?

    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...
  6. C

    Hard power series and initial value problem question

    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...
  7. B

    The initial mass function (IMF) of main-sequence stars,

    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...
  8. R

    Finding the initial velocity using quadratic

    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...
  9. C

    Finding Initial Velocity for Projectile Launch at Angle Theta

    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.
  10. M

    Calculate reservoir pore volume in field units and initial gas in place?

    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 =...
  11. G

    Initial Pressure: Calculate Using PV=nRT

    [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...
  12. J

    Physics Heat Ice Water Mixture Question And Find Initial Mass Of Ice

    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...
  13. U

    Initial conditions for BH in GR

    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!
  14. M

    Collisions: Ball with initial velocity is kicked, force of kick?

    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...
  15. T

    What are the initial conditions in this simple RCL circuit?

    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...
  16. X

    Guessing functions given initial conditions

    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 -...
  17. D

    Find s(t) Given Initial Conditions and F(s)

    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...
  18. H

    MATLAB How to build a non-uniform initial temperature with Matlab and COMSOL-thanks

    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...
  19. B

    Percent of initial total mechanical energy lost during a round trip?

    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...
  20. B

    Question on the influence of inconsistent initial values on solving periodic IVP

    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...
  21. G

    Initial value problem of ord diff eq

    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...
  22. B

    Block On Incline Projected Up With Initial Speed

    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...
  23. S

    Two questions: Initial velocity and vehicle stopping distance

    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...
  24. K

    Cannon Recoil and Initial Velocity

    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...
  25. R

    Find initial velocity using rate of climb

    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...
  26. L

    Initial value problem Euler equation

    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.
  27. M

    Cauchy problem/characteristics method with initial condition on ellipse

    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...
  28. C

    Mathematica Mathematica: NDSolve with InterpolatingFunction as initial conditions

    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...
  29. T

    What was the initial velocity of a curling stone released at the hog line?

    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...
  30. E

    How can I solve this first order DE with initial value y(0)=3^(1/2)/2?

    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?
  31. M

    Solution satisfying initial conditions for a pde of second order

    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) +...
  32. A

    Initial value inhomogeneous differential equation

    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...
  33. M

    Using initial conditions in a second order PDE

    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 +...
  34. A

    What Must Superman's Initial Velocity Be to Save the Falling Student?

    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...
  35. L

    Strategies for Solving Differential Equations Missing the Dependent Variable

    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...
  36. V

    Finding t for projectile motion without initial velocity

    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...
  37. K

    H20 Molecular shift - what is the initial state just below the Dew Point

    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...
  38. Phrak

    Initial Conditions in Classical Physics

    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...
  39. K

    What is the Initial Speed of a Baseball Thrown at a 45° Angle?

    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...
  40. C

    Initial Velocity and Inclined Plane

    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...
  41. D

    Finding initial velocity given displacement, time, and final velocity

    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...
  42. A

    Initial Velocity of a Projectile

    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...
  43. V

    What is the skier's initial velocity?

    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...
  44. rcgldr

    Show PE to KE change in closed system is independent of initial velocity

    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...
  45. D

    Help with trajectory(Finding initial velocity)

    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...
  46. B

    What are the rules for initial value problems?

    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?
  47. A

    A rock is THROWN downward. What was the initial height?

    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...
  48. D

    Calculating Initial Velocity for Symmetric Projectile Motion

    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.
  49. K

    Finding initial velocity of a free-falling object that launched off a cliff

    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...
  50. A

    Initial velocity when given distance and acceleration

    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...
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