Solve for paraboloid and Hyperboloid. 

A particle of mass m moves along a curve given in the table below At any time t, discuss the following points of the system in detail. a) An appropriate figure. b) Are there any constraints in the system? If yes mention it. c) Degree of freedom. d) Position vector. e) Velocity. f) Acceleration g) Kinetic energy h) Potential energy i) Generalized coordinates j) Lagrangian k) E. Lagrange's equations of motion 1) Conservation of total energy of the system. RECTANGULAR CYLINDRICAL SPHERICAL CONE z= x + y z=r 6 = /4 CYLINDER x + y = 1 r=1 p = csc o SPHERE x + y +2 = 1 22=1-2 p=1 PARABOLOID z = x + y z=r p= cos csc6 HYPERBOLOID x + y z = 1 2=22-1 p = -sec 20