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In the remaining exercises use multiple Fourier series to solve the BVP (double series except in ...
Use Fourier transform to solve the following BVP Utt-Uxx=F(x,t) 0<x<1,t>0u(x,0)=f(x)ut(x,0)=0u(0,t)=ux(1,t)=0
(2) Solve the following BVP for the Wave Equation using the Fourier Series solution formulae. (432 – )u(x, t) = 0 (x, t) € (0,5) x (0,0) (0,t) = 0 t> 0 Zu (5, t) = 0 to u(x,0) = sin(7x) – 12sin(77x) ut(x,0)=0
Exercise 9. Solve the BVP a(0, t) = 0 u(r, t)-Uz(n, t) = 0 u(z, 0) = sin z 0<x<π, t>0, t >0 t > 0 (z,0) = 0 2
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
get the coefficents of the fourier series in terms of an
intigral
mts) Separate variables and find Xn(x),Tn (t) for Uz = 3uxx ux(0,t) = 0, u(1,t) = 0 u(x,0) = x(1 - x) the Fourier series in terms of an integral.
1 & 5
Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the objective is to create a set of functions that will enable us to do the following 1. Evaluate the Fourier Series coefficients for the following periodic signal which is defined over one period to be rt)240sin (100nt) for 0ts 1/100 (6) The period is 1/100 seconds. This signal is called a full-wave rectified sinusoid, because it contains only the positive lobe of the sinusoidal...
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x (0, oo) t > 0 t > 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x...
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Exercises for Section 6.2 In Exercises 1-12 use the separation of variables method to solve the heat equation (a, t)auz(t<<l,t>0, subject to the following boundary conditions and the following initial conditions: a = V2, l = 2, u(0,t) = u(2,t)=0, and 5. 20, 0r< 1 0, a(x, 0) = rS 2. 1 1 = π, u(z, 0) = π-z, u(0, t) = uz(mt) = 0. 9.
Exercises for Section 6.2 In...