Aparticle of mass m moves along the r-axis under the influence of a time- dependent force given by fr, t) = -kret/7, where k and 7 are positive constants. (a) compute the lagrangian function. [7 points) (b) find the lagrangian equation of motion explicitly. (7 points) (c) compute the hamiltonian function in terms of the generalized coordinate and generalized momentum. (show clearly how you got this.) (7 points] (d) determine hamilton's equations of motion explicitly for this particular problem (not just general formulae). [7 points) (e) does the hamiltonian equal the total energy of the mass? explain. [6 points) (f) is the total energy of the mass conserved?