Question

A periodic function f(t) of period T=2π is defined as f(t)=2t ^2 over the period -π<t<π

i) Sketch the function over the interval -3π<t<3π

ii) Find the circular frequency w(omega) and the symmetry of the function (odd, even or neither).

iii) Determine the trigonometric Fourier coefficients for the function f(t)

iv) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number.

v) Determine the Fourier series for the function g(t)=2t^ 2 -1 over the period -π<t<π and write down its Fourier series for n=0, 1, 2, 3

Answer 1

Here we use formula of circular frequency and trigonometric Fourier coefficient to find the Fourier series.