Answered: Determine the solution of the…

Determine the solution of the one-dimensional wave equation = 0, 00 dx? c? dr? with c as a constant, under the following initial and boundary conditions: [x/b, 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

See similar textbooks

Related questions

Q: (B) Using the separation method solve the One-dimensional wave equation a'u atu ax e(0, t) = 0,…

Q: Utt = 16urg u(0, t) = u(7, t) = 0 u(x, 0) = f(x) = sin(x) – 4 sin(3) u(x, 0) = g(x) = sin(2a) 0 0 t…

A: We will solve the given wave equation by variable separable method. Let u(x,t)=X(x)T(t) is the…

Q: The solution of (1+ y?) + (t - etan-ly. =0 is: dt Select one: а. etan-ly t 3D 2 elan-ly b. tan-ly t…

Q: 25 Utt, 0 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial…

Q: Question 5: Solve the wave equation initial boundary problem by the method of separation of…

A: Consider the given partial differential equation 81uxx=utt t>0, 0<x<7…

Q: Question 5: Solve the wave equation initial boundary problem by the nethod of separation of…

A: we have 81uxx=utt Let ux,t=XxTt T''81T=X''X=-λ2 ⇒T''+81λ2T=0 .............iand X''+λ2X=0…

Q: Consider the initial boundary value problem (IBVP) for the wave equation: a²u a²u 4 at2 0 0 (1)…

Q: Let (dw/dt)= x - w be added to the standard three equations of the Lorenz Model. Which of the…

Q: The general solution of the wave equation of the form titt = Uxx, - co <x < co, t20, u(x,0) e-x,…

Q: Consider the wave problem ∞ 0, 1 – x2, -1 < x < 1, u(x, 0) = f(x) = otherwise, ди (x, 0) = 0. at a)…

Q: Find the explicit finite difference solution of the wave equation Utt 0 0, - with the boundary…

Q: 3. Solve the one-dimensional wave equation subject to the following conditions: [v(0,1)= 0, v(7,t)=…

A: Please check next steps for the solution.!

Q: Approximate the solution to the wave equation: 1 ô’u (x,t)- 16r? a (x,t)=0 for 00 167' ôx? u(0,t)=…

A: Given : wave equation ∂2u∂t2x, t-116π2∂2u∂x2x, t=0 for 0<x<0.5 and t>0subject tou0,…

Q: Let c>0 be a constant. Solve the one-dimensional wave equation Uxx=(1/c^2)U 0<x<1, with the boundry…

A: Given one-dimensional wave equation is uxx=1c2utt (1) 0<x<1 With boundary boundary…

Q: (b) Analyze the following wave equation where 0 <x < 0.9 mm and 0 <t < 0.2 s with the boundary…

A: Given ∂2u∂t2=4∂2u∂x2, 0≤x≤0.9, 0≤t≤0.2 boundary conditions u0,t=u0.9,t=0 initial condition…

Q: : 1/4 | 1/4 3/4 -1/4

Q: Consider the wave equation together with nonhomogeneous first boundary conditions and initial…

A: Non-homogeneous wave equation with boundary and initial condition is given by:utt=c2uxx ,…

Q: Find the explicit finite difference solution of the wave equation Utt – Urr = 0, 0 0, with the…

A: Consider the wave equation utt=uxx with the initial conditions ux,0=fx, utx,0=gx, 0≤x≤1 and the…

Q: 2m ôx² 2-2 x, y, z)= EYx, vy, =)

Q: Consider the inhomogeneous wave equation - c?uxx = f (x,t), Utt - where 1 ifx > 0, if x 1, on which…

A: Given equation is utt-c2uxx=fx,t. Let the solution be of the form ux,t=∑n=1∞TntXnx where Xnx are…

Q: The technique that we used to solve the time-dependent Schrodinger equation in class is known as…

A: The wave equation is given by, ∂2yx,t∂x2=1v2∂2yx,t∂t2 To find the solution of this wave equation…

Q: The solution of (1+y?)+(t- elan-ly. dy =0 is: dt %3D Select one: a. t = ce2tan-ly+ 2 %3D O b. 1 C…

A: Given the D. E

Q: Derive the D’Alembert’s solution of the one dimensional wave equation B. subject to the initial…

Q: Show that z = f(x+ at) + g(x - at) is a solution of the wave equation Əx?

Q: Solve the non-homogeneous wave equation Uee+ cos(t) U(0, t) = u(1, t) = 0 u(r, 0) = f(x) = 1– 2…

A: Given a non-homogeneous wave equation utt=uxx+cost, 0<x<1, t>0 with initial and boundary…

Q: Find the solution u(x, t) of the wave equation Au = ut in R³ x (0,00) that satisfies the initial…

A: Given the wave equation ∆u=utt in R3×(0,∞)

Q: (1) Use the D'Alembert solution method to solve the wave equation u 16- -0∞ 0, %3D 012 subject to…

Q: R/c Po () In Derive Form 3 of the thermodynamic equation: %3D Dt To C„T DT from Form 2: c, Dt 1 Dp p…

Q: B-Solve the wave equation subject to the initial conditions (a) u(x, 0) = sinx (all x) (b) (x, 0) =…

A: consider the provided question, the wave equation, ∂2u∂x2=1c2∂2u∂t2 Subject to the initial…

Q: Given that u = u(x, t) satisfies the wave equation utt = c?uxx in t> 0 and 0 0) with wave speed c =…

A: Let us start solving and determine whether it's true or false

Q: 2. Solve the wave equation c2 + dy? in two dimensional rectangular region 0 < x < L, 0 < y < H,…

A: The given problem is to solve the two dimensional wave equation partial differential equation with…

Q: Q2/ A string fixed at both ends with a unity length subjected to the given condition. Solve the…

A: Given: 1-D wave equation- ∂2u∂t2=c2∂2u∂x2 , c=1πu(x,0)=f(x)=cos x∂u∂t(x,0)=0 To solve the boundary…

Q: Q1) Solve the wave equation: at? ax? dU(x,0) Where: U(0,t) = U(1, t) = 0,- = 0,U(x,0) = 2(sinx+…

Q: Construct a solution to the wave equation ô²u(x,t) _ ô²u(x,t) Ôx? over the range 0 < x < +o and 0 <…

A: Let f(x), g(x) and h(t) denote the functions u(x,0), ∂u(x,t)∂tt=0 and u(0,t) respectively, then…

Q: Solve the 1-Dim wave equation using D'Alembert and separation of variables method, given the…

A: For the given equation of string hx=1-4x-0.52 the wave equation will be ∂2h∂t2=c2∂2h∂x2c=1 the wave…

Q: (3.2.1) Find the equilibrium (SS) solutions w(x) for the wave equation W„(1,x) = tw (t,x), 0<x < L,…

A: Given wave equation : wtt(t,x)=ζwxx(t,x) ,0<x<L ....(1) with boundary conditions: (a)…

Q: Solve the two-dimensional Laplace's equation J²u²u + dx² dy² 0 ≤ y ≤H, = cos I, subject to the…

Q: 4. Use the Laplace transformation to solve the wave equation, ‚²u I > 0, t>0 subject to the initial…

Q: 2. Solve the outgoing signal problem Utt- c²uxx=0, x > 0,- -00 < t < ∞0; ux (0,t) = s(t), -∞0 <t<…

A: From the above details we have,

Q: Find the solution of the wave equation if the initial velocity is zero and the initial deflection is…

A: Given the initial velocity is zero and the initial deflection is ux,0=fx=xL-x, 0<x<L

Q: 2.20 Find the solution of the wave equation a?u dx? dy? y > 0 with initial data u(х,0) — 1 и, (х,0)…

A: For the solution follow the next step.

Q: O Verify that the u= Cos 4t sin 22 Solution of Wave Equation with suitable -at ® Verify that the…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve the wave equation 1 8Pu Uz(0, t) = u#(1, t) = 0 4 dx2* Pu u(x, 0) = x(1– x), Ut(x, 0) =…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Consider the wave equation with mixed boundary condition 9u.0 0 0, u(t, 7) = 0, %3D uz(t,0) %3D u(0,…

Q: Solve the one-dimensional wave equation u, = c²u 0sxSn,120 subject to u = 0 when x=0 and x=7 u, =0…

Q: The technique that we used to solve the time-dependent Schrodinger equation in class is known as…

A: We have the given one dimensional wave equation is ∂2y(x,t)∂x2=1ν2∂2y(x,t)∂t2 …..(1) Let the…

Q: Consider the following problem for the wave equation with periodic boundary conditions at a = 0:…

A: Please check further steps for solution.

Q: Suppose a string of length L=1 unit satisfies the following wave equation. = 4 0 0. Suppose the…

A: Given wave equation is, ∂2u∂t2=4∂2u∂x2 This can also be written as, utt=22uxx…

Q: a) Use the d’Alembert solution to solve Pu 4- -∞ 0 | u(x, 0) = sin x, uz(x, 0) = sin x. Simplify…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

This question is from the subject "Partial Differential Equation"

Determine the solution of the one-dimensional wave equation
= 0, 0<x<a,t>0
dx? c? dr?
with c as a constant, under the following initial and boundary conditions:
x/b,
(i) ø(x, 0) = ƒ(x)={
0<xsb
(а- х)/(а-b), b<xSa
(ii)
(x, 0) = 0, 0<x<a
dt
(ii) Ф(0, 1) %3Dф(а, 1) %3D0, 120.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Suppose that a particle follows the path r(t) = 2 sin(3t) i+4 cos(3t) j. Give an equation (in the form of a formula involving x and y set equal to 0) whose whose solutions consist of the path of the particle. = 0. (Answer in terms of x and y.) Determine the velocity vector of the particle when t = T : v(7) = (Answer in terms of t.) Determine the acceleration vector of the particle whent = t : a(7) = (Answer in terms of t.)
Find the possible values of a and b in the expression u(x, t) = cos (at) sin (bx) such that it satisfies the wave equation.
Q: Show that the signal x(t) = sin(wt) is a periodic signal.
.ll zain IQ 8:59 AM O 36% Q1.jpg Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j
2. Eliminate the arbitrary constant(s) in the following equations: a. y = C₁x²2+ C₂x + C3 b. tany= C₁ cotx + C₂ c. y² = 2cx² + c² d. x²y siny Cx =
Q.4) Find the position of the hammered string of a piano at any time t, the length of the string is 2 meter and it is fixed at both ends. The wave constant c² = 2, the initial displacement of the string is zero and its initial velocity is given by function: u₂(x,0) = sin (xx)
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy = (sin(x))cos(y) dx 2 (a) y(0) = 1 y y
The two-dimensional Laplace equation, f(x,y) = 5x-9y-6 2²4 2²4 -= 0, describes potentials and steady-state temperature distributions in a plane. Show that the following function satisfies the two-dimensional Laplace equation. dx
Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.
2. Solve the Wave Equation shown in the image, subject to the given conditions. (perform the separation of variables and use the necessary equations to determine the roots for X (x) and T (t)):
The wave equation describes the motion of a waveform: 0 u/ôt? – d²u/ðx² = 0. Which of the following functions does not satisfy the wave equation? u(x, t) = sin(x)sin(t) u(x, t) = sin(x – t) + cos(x + t) u(x, t) = sin(x – t) u(x, t) = sin(x – t) + cos(x – t) - None of the functions shown.