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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 fro...
Answer needed in form summation from n=1 to infinity:
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 ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
(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...
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.
(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...
Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The de...
Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The density of the rod is ρ(x), stiffness k(x) being subjected to a force f(x, t). Let's derive the equations for axial vibrations of a rod using almped model. We express the rod niy mol 41 in as a chain of masses m,mm, connected to each other through springs as shown in the figure. Let's say each...
(a) A string of length L is stretched and fastened to two fixed points. The displacement of the string is given as S...
(a) A string of length L is stretched and fastened to two fixed points. The displacement of the string is given as Satu tali dengan panjang L diregang dan ditetapkan kedudukannya pada dua titik tetap. Sesaran tali diberikan sebagai u (x, 0) = The string is released with zero velocity. By applying the equation 02 with c2 1 and using the separation of variable method, a c2 at2 determine the subsequent motion u(x, t). Tali dilepaskan pada halaju sifar. Dengan...
Answer needed in form summation from n=1 to infinity:
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 ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
(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...
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.
(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...
Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The density of the rod is ρ(x), stiffness k(x) being subjected to a force f(x, t). Let's derive the equations for axial vibrations of a rod using almped model. We express the rod niy mol 41 in as a chain of masses m,mm, connected to each other through springs as shown in the figure. Let's say each...
(a) A string of length L is stretched and fastened to two fixed points. The displacement of the string is given as Satu tali dengan panjang L diregang dan ditetapkan kedudukannya pada dua titik tetap. Sesaran tali diberikan sebagai u (x, 0) = The string is released with zero velocity. By applying the equation 02 with c2 1 and using the separation of variable method, a c2 at2 determine the subsequent motion u(x, t). Tali dilepaskan pada halaju sifar. Dengan...
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