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. karush

    MHB -2.4.2 interval of initial value problem

    Determine an interval in which the solution of the given initial value problem is certain to exist $t(t-4)y'+y=0 \quad y(2)=2\quad 0<t<4$ ok my first step was isolate y' s $y'=-\dfrac{y}{t(t-4)}$ not sure what direction to go since we are concerned about an interval
  2. jaumzaum

    Why we jump with the same initial speed on 2 different planets?

    In every single question asking about the maximum height you get from jumping in 2 different planets they consider that the speed you leave the ground is constant. Why is that? Speed would be constant if impulse were constant. Impulse would be constant if both force and time were constants...
  3. peace

    Estimate the initial velocity of the cars after the collision

    What came to my mind for this question is: Consider one of the cars. The velocity and mass of this car are V and M respectively. And the velocity and mass of the piece attached to the car are m, v respectively. Before the collision, the velocity of this piece relative to this car is zero. So its...
  4. jisbon

    Engineering S-domain analysis with initial conditions

    I've attempted this questions after understanding the theory from my lecture notes, but my equation is looking bizarre here. Is this correct so far? Are my mesh equations correct here? Thanks.
  5. S

    Mechanics: Find the minimum initial velocity and angle of this projectile

    Attempt at solution in attachment.
  6. M

    How to 'shift' Fourier series to match the initial condition of this PDE?

    Hi, Question: If we have an initial condition, valid for -L \leq x \leq L : f(x) = \frac{40x}{L} how can I utilise a know Fourier series to get to the solution without doing the integration (I know the integral isn't tricky, but still this method might help out in other situations)? We are...
  7. Riccardo Marinelli

    Initial condition of Wave functions with Yukawa Potential

    Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1...
  8. T

    ADM formulation Initial Value Problem data per spacepoint

    I'm having a bit of trouble getting a clear picture of what is going on here, so if anyone can shed any light, it will be greatly appreciated. 1. I can see how the metric coefficients provide the six numbers per spacepoint, but it can't always be possible to transform the metric into a diagonal...
  9. karush

    MHB Solving an Initial Value Problem Analytically

    Solve the initial value problem $y'=\dfrac{1+3x^2}{3y^2-6y}, \quad y(0)=1$ Solving analytically $3y^2-6y\ dy = 1+3x^2 \ dx$ so far hopefully...
  10. H

    Effect of initial stress on the natural frequency of vibration

    Hello all, We might have observed that by tightening a string of a musical instrument, the natural frequency of the string changes. But I can not describe this phenomenon by the theory of linear elasticity. Also if we simulate the vibration of a bar with the help of structural software tools...
  11. jamiebean

    The final velocity = initial velocity + acceleration x time

    I first calculated initial velocity: √7.09^2+1.07^2=7.17028 acceleration=√7.22^2+2.47^2= 7.63 then i substituted all values into this equation: final velocity=initial velocity + acceleration x time so, final velocity=82.0285 so the magnitude= final velocity-initial velocity= 74.858271 is...
  12. Tymofei

    Influence of initial shift on undamped frictionless forced oscillations

    I have general equation for undamped forced oscillations (no friction) which is: I just wonder about,what type of motion should occur when initial conditions are both 0 (i.e v0=0 and x0=0). My intuitive expectation is that as there is no 'natural' oscillations at beginning,vibration has to be...
  13. karush

    MHB DE 2.1.1.16 Find the solution of the give initial value problem

    Find the solution of the give initial value problem $\displaystyle y^\prime - \frac{2}{t}y =\frac{\cos{t}}{t^2}; \quad y{(\pi)}=0, \quad t>0$$u(t)=e^{2 \ln{t}}$then $\displaystyle e^{2\ln{t}}\, y^\prime - \frac{2e^{e^{2\ln{t}}}}{t}y = \frac{e^{2\ln{t}}\cos{t}}{t^2}$not sure actually!
  14. Physics Dad

    Initial Mass Function Problem

    Assumptions: 1) The minimum stellar mass in this cluster is 0.1M⊙ 2) The maximum stellar mass in this cluster is 150⊙ First calculate the local stellar density constant (ξ0) for this cluster using eq 1: Having rearranged this equation and using the limits of the minimum and maximum stellar...
  15. M

    MHB Method of least square: initial position & velocity

    Hey! :o A point is moving linearly with constant velocity $v$ and the movement is $x=a+vt$. The below information is given: Find the initial position $a$ and the velocity using the method of least square. Could you give me a hint how we use this method here? Couldn't we use the data of...
  16. W

    I Who was the first to find an initial singularity in GR models of the universe?

    I have a question about the history of cosmology, hope its okay to ask here. Who was the first person since Einstein's Gr to point out a singularity in cosmology? I know Freidman talked of an expanding universe and Lematire a primeval atom. But were there any explicit mentions of the density of...
  17. RoloJosh16

    Find the initial acceleration in a system

    Let´ s call ##N_x## the magnitud of the force between the rod and the box and ## N_y## the magnitud of the force between the rod and the surface. ##N_x = ma_c## ##N_x= ma_r## ##mg-N_y=ma_y## The following I think is to find a relation between ##a_r## and ##a_y## and that can be found by...
  18. patricio ramos

    Question about initial and boundary conditions with the heat equation

    I am seeing the heat conduction differential equation, and I was wondering about a boundary condition when the equation is of transient (unsteady) nature. When analyzing boundary conditions at the surface of say, a sphere, the temperature does not depend on time. For example, if you have...
  19. iamcgettigan

    How do you find the initial velocity of a projectile given angle/distance?

    I tried resolving the information given into vertical and horizontal components. I then tried to find time, as this is how I would find the initial velocity. However, I am unsure of how to use the angle in this problem to help solve it. I am also unsure of how to find the initial velocity only...
  20. L

    Initial velocity given time and angle

    From Ball 1 I can can determine it's initial velocity and then maximum height. I'm not sure how this is relevant, as I cannot find a formula using angle, time, height and velocity. I have found h=V(squared) x sin (squared) Theta / 2g and also t=2Vsin Theta/g. These give similar, but different...
  21. wicker558

    Object thrown at an angle: Initial velocity has to equal speed at t

    My solution is very sketchy, but we want the math right. However, I've came to 2 thoughts that helped me get to the solution, and those are: The only way that you can launch a ball at a velocity and have it be the same velocity two seconds later, is if it's already reached its maximum height...
  22. H

    I How did the initial dust particles form?

    I've looked for a while and can't find an answer to this, hence the post. Ultimately this is a question about how the first pieces of "classical" matter formed from quantum matter. My study of self-organizing systems shows that you need a hierarchical build-up of structures to allow a complex...
  23. karush

    MHB 303 AP calculus int with initial value

    ok image to avoid typo... try to solve before looking at suggested solutions ok I think you could do this by observation if you are careful with signs
  24. Joa

    A Finding initial conditions

    Hello, I am trying to solve a differential equation corresponding to a visco-elastic material model consisting of 5 units of springs and dashpots connected in parallel as can be seen in the image below. I am able to come-up with a single fifth order ODE, however I am struggling to find the...
  25. S

    Calculating the initial frequency of a decelerating flywheel

    I converted 5 minutes to 300 seconds, and movement angle per second as shown on the picture. From here on I am lost, as the angular velocity can't be calculated, as the time given isn't the one in which the flywheel does one rotation. I apologise if I used any expressions wrong, english is not...
  26. zizzle

    Minimum initial speed to spin a particle around a disk (with gravity)

    For this problem, since the weight force on the "particle" (child) is not always aligned with the tangential circular path of the disks, I couldn't think of a way to use rotational kinematics equations. As such, I tried to solve the problem using work principles (namely, that the change in...
  27. Quantum Alchemy

    B How constrained are the initial conditions of the universe?

    Do we know? Do we have any idea? There seems to be 2 schools of thought. 1. The initial conditions can be almost any value with universes inflating with different laws of physics. This is the multiverse and string theory 10^500 false vacua view. 2. The initial conditions are more restrained...
  28. T

    I Does Euclidean geometry require initial fine-tuning?

    https://en.wikipedia.org/wiki/Flatness_problem The flatness problem (also known as the oldness problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. The fine-tuning problem of the last century was solved by introducing the theory of inflation which flattens...
  29. Like Tony Stark

    Initial conditions in simple harmonic motion

    I have the formula for amplitude ##A=\sqrt (x_0^2 + \frac{\dot x_0 ^2}{\omega^2})##. But ##x_0## and ##\dot x_0## refers to the initial conditions, and the information that I'm given is not related to the initial conditions, or at least I'm not told so.
  30. K

    Closest approach from initial velocity and impact parameter

    Here were my assumptions: Energy and angular momentum are both conserved because the only force acting here is a central force. The initial angular momentum of this particle is ##L = mv_0b## and we can treat E as a constant in the homework equation given above. I solved for the KE (1/2 mv^2) in...
  31. A

    Projectile Motion with Unknown Initial Height

    First, I tried solving for the total time of flight, which I got as 100 = 5cos25*t --> t=22 s Since we know the height at which the object lands, but not at which it is launched, I tried setting up the equation as: yf = 40 - y0 = y0 + 5sin25*(22) - 1/2(9.8)(22)^2 However, I got y0 = 1183 m...
  32. L

    Is the initial dark carbon water from a purifier safe to drink?

    Please see attached pictures. Whenever we replace the right cartridge (with carbon filter) with new one (every 6 months). There are initial dark tint water from the carbon that fills a basin. Are the dark water safe? We throw the water of course. But there maybe those who didn't know or have...
  33. karush

    MHB Cp2.63 find the initial velocity

    cp2.63. The acceleration of a particle is given by $$a(t)=-2.00 \, m/s^2 +3.00 \, m/s^3.$$ a. find the initial velocity $v_0$ such that the particle will have the same x-coordinate at $t=4.00\, s$ as it had at $t=0$. b. What will be the velocity at $t=4.00 s$ ok sorry but I don't even know...
  34. karush

    MHB 31.6 Solve the initial value problem

    $\tiny{31.6}$ Solve the initial value problem $Y'=\left|\begin{array}{rr}2 & 1 \\-1 & 2 \end{array}\right|Y +\left|\begin{array}{rr}e^x \\0 \end{array}\right|, \quad Y(0)=\left|\begin{array}{rr} 1 \\1 \end{array}\right| $ ok so we have the form $y'=AY+G$ rewrite as $$\displaystyle...
  35. T

    Initial Value Equations from ADM Formalism - Trying again

    ##\delta(- N\mathcal{H}) = \delta(-N[\gamma^{-\frac{1}{2}}(Trπ ^2 - \frac{1}{2}(Trπ )^2 -\gamma^{\frac{1}{2}}R])## and I am going to concentrate on the first part and find ##\delta(-N[\gamma^{-\frac{1}{2}}(Trπ ^2 - \frac{1}{2}(Trπ )^2]) ## wrt ##g_{ij}##. ##\delta(-N[\gamma^{-\frac{1}{2}}(Trπ...
  36. karush

    MHB 3.1.11 find the solution of the given initial value problem:

    find the solution of the given initial value problem: $6y''-5y'+y=0\quad y(0)=4 \quad y'(0)=0$ if $r=e^{5t}$ then $\displaystyle 6y''-5y'+y=(r-3)(r-2)=0$ then $y=c_1e^{3t}+c_1e^{2t}=0$ for $y(0)=4$ $y(0)=c_1e^{3(0)}+c_1e^{2(0)}=4$ ok I don't see how the last few steps lead to the...
  37. A

    Calculate the difference between initial and the final masses

    Don't really know how to go about this exercise as I've been given no information for it I tried googling similar problems but couldn't find any If someone could give me a process to try I will then try to solve it here in this section, thanks.
  38. cianfa72

    Daniell cell initial equilibrium

    Hello, consider again a simple Daniell cell with salt bridge in place but no external electric connection between electrodes. Reading from some source e.g. link1 it seems upon Zinc and Copper metal rods are dipped into their own ions solution, both will gain a negative charge (-) due to an...
  39. T

    Initial Value Equations out of ADM formalism

    In my earlier post, I demonstrated a way to derive MTW's Equation (21.90), ##16π\mathfrak{L}_{geom} = - \dot π^{ij} γ_{ij} - N\mathcal{H} -N_i\mathcal{H^i}-2(π^{ij}N_j-½N^iTrπ+γ^½N^{|i})_{,i}## MTW (21.90) I received my first two 'likes' for this which made me really happy - Thanks...
  40. pluralangel

    seeking help finding the initial velocity of a type 3 projectile

    hi, so I've been trying to find the initial velocity of this projectile; but i ended up getting a negative value for seconds squared. I've gone over my solution multiple times but don't see where i went wrong. alternatively, was i supposed to take the absolute value of seconds squared? thanks...
  41. opus

    Initial Value w/ Vector-Valued Function

    From ##\vec r''(t)## we integrate to get $$\vec r'(t) = \left(-\sin(t)+C_1\right)\hat i + \left(6\cos(2t)+C_2\right)\hat j - \left(9.8t+C_3\right)\hat k$$ Solving for the C constants using ##\vec r'(0) = 1\hat i + 6\hat j + 0\hat k##, ##\vec r'(0) = <C_1, C_2, C_3>## ##=<1, 6, 0>## So we now...
  42. Josh chips

    Find the initial velocity of the second stone

    since the question states they hit the ground at the same time i firs find the time they hit the ground y= ut + 1/2at^2 initial velocity is 0 for the first stone 320= 0 + 4.9t^2 this t= 8 secs since the 2nd stone was thrown 100 m below stone 1 distance from ground is 220m 220 = ut -...
  43. J

    Initial states ppbar can proceed to npi^0 with parity conserved

    I'm working on some stuff for particle physics and I had a few questions I wanted to ask . Heres the outline of the problem : Establish which initial states of the ppbar system amongst 1^S_0, 3^S_1, 1^P_1, 3^P_0, 3^P_1, 3^P_2, 1^D_2, 3^D_1, 3^D_2, 3^D_3 the reaction ppbar->npi^0 can...
  44. C

    Engineering Advanced Circuits, Laplace Transform, Find Initial Conditions

    Vo(S) = [ N(s)Vi(s) + (- s2 + s - 2) ] / s3 + s2 + 1 ; can ignore (-s^2 + s - 2). From relevant equations: Vo(S) = [N(s)*Vi(s)]/(s^3 + s^2 + 1); -> (d3Vo(t)/dt3) + (d2Vo(t)/dt2) + Vo(t) = N(t)(dvi)/dt L[vi(t)] = t to s domain: [s3Vo(s) - s2Vo(0-) - SV'o(0-) - Vo''(0-)]Vo(s) + s2 - SVo -...
  45. T

    How to find initial velocity with only an angle and distance?

    I am in Algebra 2 and the homework asks a question: "You and a friend arw driving golf balls at a driving range. If the angle of elevation is 30 degrees and the ball travels 625 feet horizontally, what is the initial velocity of the ball?"
  46. C

    About initial mass function and mean mass in stellar cluster

    Homework Statement Assuming a Salpeter IMF with upper and lower mass limits of 0.1 and 20 M⊙ respectively, calculate: (i) the mass point at which half the mass formed in a stellar cluster lies in more massive systems and half in less massive systems. ii) the mass point at which half the...
  47. jk22

    I Averaging Initial & Endstates in Trace Formula

    Basically the question is : since the experiments are repeated and results averaged, should not initial and endstates be mixed states ? So now we should give two density matrices, so how do we average like in the trace formula : ##\langle A\rangle=tr(\rho A)## ? Is it ##\rho=\sum_i...
  48. pellman

    I How can one know the initial state from measurements?

    Theoretical problems often begin with "given a system in state ψ0" For example, the 2-slit experiment begins with the assumption of a plane wave incident on the slits. I had always understood to this mean some prior set of measurements had been made to determine the initial state. But how can...
  49. V

    Solve the initial value problem

    Homework Statement Solve the initial value problem y1'=-13y1+4y2 y2'=-24y1+7y2 y1(0)=5, y2(0)=2 Homework EquationsThe Attempt at a Solution Here is what I have: y'=[-13 4, -24 7]y I change it to A=[-13 4, -24 7] My eigenvalues are λ=-1 and λ=-5. My basis are [1/3 1] and [1/2 1]. Now I have...
  50. R

    Space elevator minimum initial speed

    Homework Statement In the far future, humans have built a space elevator as a cheap means of access to space. However before that could be done, a few basic principles had to be worked out. . . a) What is the minimum initial speed (in an Earth-centered inertial reference frame) needed for an...
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