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

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'' + \omega^2 𝑦 = r(t) $, where $ r(t) = |t|, -\pi < t < \pi $ by using Fourier series.

So far I have set up the ODE and set equal to r[t]

r[t] = y''[t] + ω^2 y[t]
Plot(r[t], {t, -π, π}]

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