7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor- dinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an ad- ditional force f= -Arª-¹ directed toward the origin (r is the distance from the origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi- nates, and find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Explain.

7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor- dinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an ad- ditional force f= -Arª-¹ directed toward the origin (r is the distance from the origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi- nates, and find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Explain.