# Homework Help: Fourier series of periodic function

1. Nov 29, 2015

### masterchiefo

1. The problem statement, all variables and given/known data
Periodic function P=3
f(t) = 0 if 0<t<1
1 if 1<t<2
0 if 2<t<3
a) Draw the graph of the function in the interval of [-3,6]

b) Calculate the Fourier series of f(x) by calculating the coefficient.

2. Relevant equations

3. The attempt at a solution
a) in attached file

b)
How do I know what is my L?
L=3/2

$\text{ao} = \frac1L \int_0^{3} \left( f(x) \right) dx$
$\text{ao} = \frac1L \int_0^{1} \left( 0 \right) dx + \frac11 \int_1^{2} \left( 1 \right) dx + \frac11 \int_2^{3} \left( 0 \right) dx$
ao=2/3

$\text{an} = \frac1L \int_1^{2} \left( 1cos(n*pi)/L*x) \right) dx$ n>=1
an= sin(2*n*pi)/n*pi -sin(n*pi)/n*pi

$\text{an} = \frac1L \int_1^{2} \left( 1sin((n*pi)/L*x) \right) dx$ n>=1
bn= cos(n*pi)/n*pi - cos(2*n*pi)/n*pi

#### Attached Files:

• ###### question100.jpg
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Last edited: Nov 29, 2015
2. Nov 29, 2015

### LCKurtz

You haven't told us what P is. I suppose it is the period. If so, the P = 3. You also haven't told us what L is defined as. Is it half the period? If so then L = 3/2.

3. Nov 29, 2015

### masterchiefo

okay, after I change L for the correct value, is the steps good ?
is my graph good ?

4. Nov 29, 2015