The Fourier series representation, FS(t)FS(t), of a function f(t)f(t), where f(t+4)=f(t)f(t+4)=f(t) is given by FS(t)=a0/2+∞∑n=1an cos(nπt2)+bnsin(nπt/2) In this particular case the Fourier series coeffcients are given by a0=0.75a0=0.75 an=6(−1)n/nπ bn=2(1−2(−1)n)/n2π2 Compute the Fourier series coefficients for n=1,2,3n=1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS3(3)FS3(3) correct to 3 decimal places.
The Fourier series representation, FS(t)FS(t), of a function f(t)f(t),
where f(t+4)=f(t)f(t+4)=f(t) is given by
FS(t)=a0/2+∞∑n=1an cos(nπt2)+bnsin(nπt/2)
In this particular case the Fourier series coeffcients are given by
a0=0.75a0=0.75
an=6(−1)n/nπ
bn=2(1−2(−1)n)/n2π2
Compute the Fourier series coefficients for n=1,2,3n=1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS3(3)FS3(3) correct to 3 decimal places.
Enter the values in the boxes below.
Enter a1 correct to 4 decimal places:
Enter a2 correct to 4 decimal places:
Enter a3 correct to 4 decimal places:
Enter b1 correct to 4 decimal places:
Enter b2 correct to 4 decimal places:
Enter b3 correct to 4 decimal places:
Enter FS3(3)) correct to 3 decimal places:
Step by step
Solved in 2 steps with 2 images
