I am having trouble finding the Fourier series of a 2nd order ODE. Should I be using the piecewise function as well to set up the range for t?

Solve 𝑦′′ + 𝜔^2𝑦 = 𝑟(𝑡), where 𝑟(𝑡) = |𝑡|, -𝜋 < 𝑡 < 𝜋 using Fourier series

So far I have set up the ode and set equal to r(t)

`r(t)=y''(t)+omega^2*y(t)`

`Plot(r(t),{t,-Pi,Pi})`

Any help with the mathematica code would be greatly appreciated. How can I find An, Bn with the function being an ODE