Need a good explanation for Part B thanks Linear Oscillator

Need a good explanation for Part B, thanks!

Linear Oscillator with Periodic Forcing. Consider the second-order differential equation, y\" + 4y = f(t) where f(t) is the periodic square wave shown in the figure. (a) Verify that the Fourier trigonometric series for f(t) has the form, f(t) = a_0/2 + sigma^infinity_j = 1 b_2j-1 sin(2j-1)t). Determine the coefficients a_0 and b_2j-1. (use the interval [-pi, pi] to calculate the Fourier Series.) (b) Find a series representation for the general solution for each term in the Fourier series for f(t) and then summing these results to get a (formal) solution for f(t). Use undetermined coefficients to find the particular solutions.

Solution

http://web.mit.edu/2.14/www/Handouts/FreqDom.pdf