Lagrangian of 1D Motion: Finding Particle Coordinate x at Time t

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To find the coordinate x of a particle in 1D motion using the Lagrangian, one must apply the Euler-Lagrange equation to the Lagrangian of the system. This process results in a differential equation involving the function f(x). Solving this differential equation will yield the function f(x), which describes the particle's position over time. The key step is correctly formulating the Lagrangian and applying it to the Euler-Lagrange framework. Ultimately, solving the differential equation provides the necessary coordinate x at time t.
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i have L of particle m in 1D motion, but how i can find the coordinate of particle x at time t?
 

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