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【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/1Coordinates in general:The right generalised coordinates for this system are two-dimensional and can be chosen as the position of the particle in the x-y plane: x = x(t) and y = y(t) (t).Equations of Motion Based on Lagrangians:The system's Lagrangian is the difference between its kinetic energy and its potential energy.L = T - Uwhere T is the energy of motion and U is the energy of potential motion.How fast the particle is moving is given byT = ½mv²where m is the particle's mass and v is its speed.The particle's potential energy due to the gravity field is given byU = mgzwhere g is the acceleration caused by gravity and z is the particle's height above the origin.The particle's potential energy due to the extra force is given byU = -Ar-awhere A and an are constants and r is the dista ... See the full answer