1. Solve the following problems using Fourier Series, assuming L = 1: y" + 4π2y = cos(nt) 1n F(t)...
1. Solve the following problems using Fourier Series, assuming L = 1: y" + 4π2y = cos(nt) 1n F(t)-ΊΟ, t < 0 1, t20 " y+ 2y F(t), where
please complete all parts Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral: Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
plz 1. Let and y be the Fourier series coefficients of r(t) and y(t), respectively. Assuming the period of r(t) is T, express y in terms of d (b) y(t) (10 pts) () (a) y(t) (at), where a 0. (10 pts) dt 1. Let and y be the Fourier series coefficients of r(t) and y(t), respectively. Assuming the period of r(t) is T, express y in terms of d (b) y(t) (10 pts) () (a) y(t) (at), where a 0....
solve using Laplace transforms (f) y"+y=f(t – 37) cos(t), y(0) = 0, y'(0) = 1. (g) y" + 2y = U(t – 7) +38(t – 37/2) – Ut – 27), y(0) = y'(0) = 0.
dt - Solve the following equation for y(t) using Fourier Transforms. dy(t) ? +2y(t) = { 'h(t) where h(t) is the Heaviside function: (0,t=0 h(t)= | 1,20 Note: the solution satisfies ly(t) >0 as t →+00.
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)...
(1 point) Find the Fourier series expansion, i.e., f(x) [an cos(170) + by sin(t, x)] n1 J1 0< for the function f(1) = 30 < <3 <0 on - SIST ao = 1 an = cos npix bn = Thus the Fourier series can be written as f() = 1/2
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 < L, t>0} subject to the boundary conditions (0, t) (L, t) (x,0) f(x) 8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 0} subject to the boundary conditions (0, t)...
Write the Fourier Series of the function f (t) = | cos (t) | for t defined on the interval [−π, π].
Find a Fourier series expansion of the periodic function 0 -T -asts 2 - f(t) = 6 cost T <<- 2 2 0 I SISE 2 f(t) = f (t +21) Select one: a f(t)= 12 12 5 (-1)** cos nt 1 2n-1 b. f(t) = 12.12 F(-1)** cos 2nt T 4n-1 C 6 12 =+ 125 (-1) C05 211 472-1 6 12 (-1) * cosm d