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. A

    Partial Differential Equation with initial conditions

    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...
  2. M

    A question about uniqueness of initial conditions

    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.
  3. R

    Initial condition effect in Nonlinear PDE of a wave

    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...
  4. Art_Vandelay

    Imagine that a bullet is shot vertically into the air with an initial

    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...
  5. S

    Calculating Initial Speed of a Meteorite Based on Energy Transformations

    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...
  6. A

    How Does Physics Apply in the New Olympic Sled and Spring Event?

    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...
  7. S

    MHB Looking at a solitary initial state

    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...
  8. P

    Threaded connection's initial contact modelling using ANSYS workbench

    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...
  9. D

    Tennis ball's final velocity without it's initial

    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...
  10. N

    Finding initial wavelength of photo given angle of deflection

    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...
  11. G

    Find Initial Velocity of Projectile Basketball

    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...
  12. A

    Fortran How are the initial X values chosen? Fortran

    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...
  13. M

    MHB Initial and boundary value problem

    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...
  14. J

    Solving an Initial Value Problem with Separable Differential Equations

    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) =...
  15. I

    Engineering The Mystery of the Inductor's Initial Current

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

    Prove this equation of initial velocity in projectile motion

    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...
  17. M

    MHB Word problem: initial height of projectile

    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...
  18. H

    Differential Equation Initial Value Problem

    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...
  19. M

    Simple pendulum with initial velocity

    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...
  20. K

    Calculating time to arbitrary points of distance with initial velocity

    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...
  21. T

    Working out the initial velocity

    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...
  22. P

    Reducing Initial Time Step Benefits for FE Analysis

    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...
  23. O

    MHB Uniqueness of Solution for x' = f(x) = √(1-x^2), x(2) = 1

    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)...
  24. N

    Stone throw find initial speed

    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...
  25. S

    MHB Solving the Initial Value Problem for x'=x^3 with x(0)=1

    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...
  26. M

    Initial Energy/Final energy on 2 capacitors

    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...
  27. M

    Homogeneous initial value problem

    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...
  28. G

    Definition of a Gaussian wave packet for a Initial State

    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...
  29. Y

    MHB Solve Recurrence Relation w/ 3 Terms & Initial Conditions

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

    Initial acceleration of block when string is cut

    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...
  31. D

    Engineering Solving RL Circuit Differential Equation: Initial Conditions

    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...
  32. Eagle9

    Where do the initial neutrons come from?

    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...
  33. H

    Initial Data for General Relativity: EFE

    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?
  34. J

    Initial Value problem 1st order ODE

    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...
  35. I

    Time independent wave function vs the initial wave function

    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
  36. A

    Laplace transform initial value problem-

    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...
  37. Vanrichten

    MHB Phase Line and long term behavior with initial value

    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 di fferential equation with...
  38. Z

    Burgers Equation Question - cannot satisfy initial conditions

    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...
  39. alexsylvanus

    Separable Differential Equations Using Initial Values

    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...
  40. D

    Determine the minimum initial velocity

    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)...
  41. J

    Solve for the initial value of the differential equation

    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...
  42. MattRob

    Change in Vrms, given initial P and V, find energy added.

    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...
  43. evinda

    MHB Does B accepts the language L',no matter which is the initial automaton A?

    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...
  44. J

    Explanation of E-field torque and initial angle

    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...
  45. PsychonautQQ

    Seperable DE with Initial Condition

    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...
  46. P

    Calculate Initial Speed of Ball Thrown Vertically 14m in 3s

    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...
  47. L

    Calculating initial trajectory without time

    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...
  48. M

    Calculating Initial Velocity of a Basketball Shot

    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...
  49. Z

    Dimensional Analysis with non-dimensional initial parameter

    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.)...
  50. J

    How is the initial conditions for PDE?

    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...
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