sandy.bridge
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Homework Statement
-0.5\leq{t}\leq{1.5}, T=2
The wave is the attached picture.
I need to determine the Fourier Series of the wave in the picture.
I know that f(t)=a_0+{\sum}_{n=1}^{\infty}a_ncos(n\omega_0t)+{\sum}_{n=1}^{\infty}b_nsin(n\omega_0t)
where a_0=\bar{f}=0 due to being an even function. Furthermore, b_n=0 due to being an even function also.
That leaves,
a_n=\int_{-0.5}^{0.5}cos(n\omega_0t)dt-\int_{0.5}^{1.5}cos(n{\omega}_0t)dt=0-\frac{1}{n\omega_0}(sin(1.5n{\omega}_0t)-sin(0.5n{\omega}_0t))=\frac{1}{n{\omega}_0}(sin(0.5n{\omega}_0t)-sin(1.5n{\omega}_0t))
therefore,
f(t)=\frac{1}{{\omega}_0}\sum_{n=1}^{\infty}cos(n{\omega}_0t)(sin(0.5n{\omega}_0t)-sin(1.5n{\omega}_0t))
Is this suffice as an answer, or am I missing something? My textbook is lacking examples so I just would like to know if I am doing it right. Thanks!