Solving this spring mass system using differential equations

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To be honest I dont know how to do this problem, I only know that we should get a second order linear differention equation for the position $x$. And we have to solve the problem using theta.

I know that $X(t)= r\sin\theta$, where r would be the length of the rod but I dont know where to go from there. Were also given that the Lagrangian function is L= T-V, But im not sure what to do with this.

Can someone please provide a step by step explanation of how they would solve this problem?

I really want to understand the solution and not just be given a direct solution please.

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