Question

Find the Fourier series of ? up to the second harmonic from the following table:

x | 0 | 2 | 4 | 6 | 8 | 10 | 12 |

y | 9.0 | 18.2 | 24.4 | 27.8 | 27.5 | 22.0 | 9.0 |

Answer #1

Find the Fourier series for the following function (which has
period 4): f(x) = −x−2 if −2<x<0
−x + 2 if 0 < x < 2

Find the:
(a) Fourier cosine series
(b) Fourier sine series
for the following shape using half range expressions
f(x)=x^(2), 0 less than or equal to x less than or equal to
1

Find the Fourier cosine series and sine series, respectively,
for the even and odd periodic extensions of the following function:
f(x)= x if 0<x<π/2.
2 if π/2<x<π.
Graph f with its periodic extensions (up to n = 4) using
Mathematica.(leave codes here)

Find the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

Find the Fourier series for the following function (which has
period 2): f(x)= −x if −1<x<0
x if 0 < x < 1

1. Find the Fourier cosine series for f(x) = x on the interval 0
≤ x ≤ π in terms of cos(kx). Hint: Use the even extension.
2. Find the Fourier sine series for f(x) = x on the interval 0 ≤
x ≤ 1 in terms of sin(kπx). Hint: Use the odd extension.

Find the Fourier series of f(x) as given over one period.
1.
f(x) =(0 if −2 < x < 0 and
2 if 0 < x < 2 )

Find a Fourier Series expansion for the function f(x)= xcos(3x)
on the domain from x = [-pi,pi]

Find the Fourier Series of the function: f(x)=0, -5<x<0,
f(x)=3, 0<x<5 with a period=10.
Write briefly about how such a series expansion could be used?
For example, in digital to analog conversion?

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < L, t
> 0, u(0,t) = 0 = u(L,t), u(x,0) = x(L - x)2,
ut(x,0) = 0

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