Solve coupled 2nd order ODE

Hi guys,
I got two second order equations that look like this with force 'F' time dependent:
I've tried numerous methods to uncouple them but with no success. I also tried using the buil-in functions such 'odeToVectorField' together with 'matlabFunction'.
Any help on how this might be done in MATLAB? Apologies if I'm missing something obvious.
Thanks in advance!

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2021-8-20

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