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Consider an elastic string of length L whose ends are held fixed. The string is set in motion fro...
Consider an elastic string of length L whose ends are held fixed. The string is set...
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity wx,0) - parts (b) and (c). (A computer algebra system is recommended.) x). Let L = 18 and 2 = 1 in g(x) = (a) Find the displacement u(x, t) for the given [x). (Use a to represent an arbitrary constant.) Ux. 1) - ECO , (h) Plot uix, t) versus x for OS...
(a) Consider an elastic string of length 10 whose ends are held fixed. The string is...
(a) Consider an elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial postion J2/4 0<x<8 u(x,0) = { 0 8 << 10 Assuming the string is elastic enough to assume this initial configuration, i. Find the Fourier sine series for f (extended as an odd periodic function of period 20). ii. Assuming the propagation speed a = 2 solve the wave equation to find the displacement...
u(x, t) represents the vertical displacement of a string of length L = 16 with wave...
u(x, t) represents the vertical displacement of a string of length L = 16 with wave equation 25uxx = uft at position x along the string and at time t Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position b. the initial velocity is a constant 5 and the vertical displacement is 0. c. the initial velocity is a constant 5 and the rightmost position is held at a vertical displacement of...
A light elastic cord of length 2l and stiffness k is held with the ends fixed...
A light elastic cord of length 2l and stiffness k is held with the ends fixed a distance 21 apart in a horizontal position. A block of mass m is then suspended from the midpoint of the cord. Show that the potential energy of the system is given by the expression: U(y) = 2k1/2-21Vy2t12-may, where y is the vertical sag of the center of the cord. From this show that the equilibrium position is given by a root of equation...
(The wave equation) Consider a string with fixed zero ends of length L with speed parameter...
(The wave equation) Consider a string with fixed zero ends of length L with speed parameter c, with initial position -X u(x,0) = x € (0, L/2] c [L/2, L] C L and zero initial velocity. (a) Find the normal modes of the solution and specify the spatial and temporal frequencies for each. (You do not need to derive the general solution to the wave equation with fixed ends.) (b) Describe how the tension Th, density p and length L...
show steps please! (1 point) u(x, t represents the vertical displacement of a string of length...
show steps please!
(1 point) u(x, t represents the vertical displacement of a string of length L = 20 with wave equation 16. time t = Utt at position x along the string and at Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position is held at a vertical displacement of 1 and released b. the initial velocity is a constant -5 and the vertical displacement is 0 c. the initial velocity...
Homework problem: Given a string fixed at both ends of length L and linear density el....
Homework problem: Given a string fixed at both ends of length L and linear density el. The string is plucked from a height h, 1/4 of the distance from the end initial velocity of all parts of the string is zero): Part 2a (20 pts): What is the equation of motion y(x,t) for this system? 01/4L Part 2b (20pts): given the trial solution y(x,t) = 2n=o(An cos(wnt) + B, sin(wnt))sin (knx), what are the values of An and Bn.
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the s...
parts a,b, c
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the string is initially at rest. The initial boundary value problem (IBVP) is written as u(0,t) -u(1,t) u(x,0) = f(x), 0 ut (z, 0-0, 0 < x < 1. The solution of this IBVP using the method of separation of variables is given by n-l a) Find the coefficients bn. b) Show that this wave function can be written as the...
Problem 2. A string of a guitar is fixed at the two ends, x = 0...
Problem 2. A string of a guitar is fixed at the two ends, x = 0 and r = a. The string is set in motion with initial position f(x) = (h/a)., 0 <r <a, where h > 0, and then it is released with no initial velocity. The displacement u of the string is described by the PDE au 1 au ar2 2 212 0<x<a, t> 0. (i) State the boundary value initial value problem that u satisfies. (ii)...
D by an elastic string from a fixed pole. The stant ink = mg/l,After being released a 5 slope,h o...
d by an elastic string from a fixed pole. The stant ink = mg/l,After being released a 5 slope,h of the string iust unstretched, the box slides down he slope. The initial from rest with the string being box slid location is chosen so that the subsequent motion is o 3. On 7 45 The box remains on the slope throughout the situations in this questions. The coefficient friction of the slope is ,where u < 1. amplitude bf the...
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity wx,0) - parts (b) and (c). (A computer algebra system is recommended.) x). Let L = 18 and 2 = 1 in g(x) = (a) Find the displacement u(x, t) for the given [x). (Use a to represent an arbitrary constant.) Ux. 1) - ECO , (h) Plot uix, t) versus x for OS...
(a) Consider an elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial postion J2/4 0<x<8 u(x,0) = { 0 8 << 10 Assuming the string is elastic enough to assume this initial configuration, i. Find the Fourier sine series for f (extended as an odd periodic function of period 20). ii. Assuming the propagation speed a = 2 solve the wave equation to find the displacement...
u(x, t) represents the vertical displacement of a string of length L = 16 with wave equation 25uxx = uft at position x along the string and at time t Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position b. the initial velocity is a constant 5 and the vertical displacement is 0. c. the initial velocity is a constant 5 and the rightmost position is held at a vertical displacement of...
A light elastic cord of length 2l and stiffness k is held with the ends fixed a distance 21 apart in a horizontal position. A block of mass m is then suspended from the midpoint of the cord. Show that the potential energy of the system is given by the expression: U(y) = 2k1/2-21Vy2t12-may, where y is the vertical sag of the center of the cord. From this show that the equilibrium position is given by a root of equation...
(The wave equation) Consider a string with fixed zero ends of length L with speed parameter c, with initial position -X u(x,0) = x € (0, L/2] c [L/2, L] C L and zero initial velocity. (a) Find the normal modes of the solution and specify the spatial and temporal frequencies for each. (You do not need to derive the general solution to the wave equation with fixed ends.) (b) Describe how the tension Th, density p and length L...
show steps please!
(1 point) u(x, t represents the vertical displacement of a string of length L = 20 with wave equation 16. time t = Utt at position x along the string and at Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position is held at a vertical displacement of 1 and released b. the initial velocity is a constant -5 and the vertical displacement is 0 c. the initial velocity...
Homework problem: Given a string fixed at both ends of length L and linear density el. The string is plucked from a height h, 1/4 of the distance from the end initial velocity of all parts of the string is zero): Part 2a (20 pts): What is the equation of motion y(x,t) for this system? 01/4L Part 2b (20pts): given the trial solution y(x,t) = 2n=o(An cos(wnt) + B, sin(wnt))sin (knx), what are the values of An and Bn.
parts a,b, c
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the string is initially at rest. The initial boundary value problem (IBVP) is written as u(0,t) -u(1,t) u(x,0) = f(x), 0 ut (z, 0-0, 0 < x < 1. The solution of this IBVP using the method of separation of variables is given by n-l a) Find the coefficients bn. b) Show that this wave function can be written as the...
Problem 2. A string of a guitar is fixed at the two ends, x = 0 and r = a. The string is set in motion with initial position f(x) = (h/a)., 0 <r <a, where h > 0, and then it is released with no initial velocity. The displacement u of the string is described by the PDE au 1 au ar2 2 212 0<x<a, t> 0. (i) State the boundary value initial value problem that u satisfies. (ii)...
d by an elastic string from a fixed pole. The stant ink = mg/l,After being released a 5 slope,h of the string iust unstretched, the box slides down he slope. The initial from rest with the string being box slid location is chosen so that the subsequent motion is o 3. On 7 45 The box remains on the slope throughout the situations in this questions. The coefficient friction of the slope is ,where u < 1. amplitude bf the...
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