Objective: Get practice with Lagrangian mechanics by solving Lagrange’s equations for another simple system for which you already know the answers.

Consider a block of mass m subject to gravity and sliding down a frictionless inclined plane making an angle with respect to the horizontal (you may ignore air resistance). Write down the Lagrangian using coordinates along the plane’s surface and perpendicular to it. Find Lagrange’s equations to obtain 2 equations of motion and verify that they match what you would expect from Newton’s laws.

Note are attached in Files a, b, c.