3. The graph of the periodic function f(t) = t cos(t), t < , f(t +...

 

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3. The graph of the periodic function f(t) = t cos(t), t < , f(t + 2) = f(t) is indicated in Figure 3. f(t) 2 321 -5 -2 Figure 3 (a) What is the period of the function? [1] (b) Use an algebraic method to determine the parity of the function. [1] (c) Calculate the constant term ao of the Fourier Series. [1] (d) Calculate the Fourier coefficients a and b. [3] [9] (e) Calculate the Fourier coefficients an and bn for n 1. [Hint: You may use the identities + sin(t) sin(nt) dt = + cos(t) cos(nt) dt = 0 for - -IT n1 and sin(t) sin(nt) dt = f** cos(t) cos(nt) dt = 0 for n 1.] 3. The graph of the periodic function f(t) = t cos(t), t < , f(t + 2) = f(t) is indicated in Figure 3. f(t) 2 321 -5 -2 Figure 3 (a) What is the period of the function? [1] (b) Use an algebraic method to determine the parity of the function. [1] (c) Calculate the constant term ao of the Fourier Series. [1] (d) Calculate the Fourier coefficients a and b. [3] [9] (e) Calculate the Fourier coefficients an and bn for n 1. [Hint: You may use the identities + sin(t) sin(nt) dt = + cos(t) cos(nt) dt = 0 for - -IT n1 and sin(t) sin(nt) dt = f** cos(t) cos(nt) dt = 0 for n 1.]