Question: 1 2 . Using the Lagrange equation and the undetermined coefficients method, find the angle ( theta _ { c } )

12. Using the Lagrange equation and the undetermined coefficients method, find the angle \(\theta_{c}\) at which an object that was at rest on the top of a path made of a \(1/4\) circle with a radius I slides down the path without friction. Assume that the magnitude of the acceleration due to gravity is \(\mathbf{g}\), and that the potential energy is based on the floor.
1 2 . Using the Lagrange equation and the

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