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Problem 2) Objective: Get practice with Lagrangian mechanics by solving Lagrange's equations for another simple system for which you already know the answers

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Problem 2) 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 in subject to gravity and sliding down a frictionless inclined plane making an angle B 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. 

Problem 4) Objective: Understand how one might modify Lagrange's equations if a non-conservative force does work on a system. 
Consider a particle moving in ID along the x axis. It is subject to a net force along the x axis given by: F = F +F., where F ax — ax is a conservative force and F.,. is a nonconservative force. Show that with 2" = T—U as usual, the Euler-Lagrange equation describing the motion becomes: 
az, d a.e +F —=0. at wars clz