Fourier series of periodic function

[masterchiefo]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

a) in attached file

b)
How do I know what is my L?
L=3/2$\text{ao} = \frac1L \int_0^{3} \left( f(x) \right) dx$
$\text{ao} = \frac1L \int_0^{1} \left( 0 \right) dx + \frac11 \int_1^{2} \left( 1 \right) dx + \frac11 \int_2^{3} \left( 0 \right) dx$
a_o=2/3

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

 

[LCKurtz]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

a) in attached file

b)
How do I know what is my L?
L=1

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.

 

[masterchiefo]

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.

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

 

[LCKurtz]

Your graph is good. I didn't check your arithmetic.