Problem number 3 (10pts) a particle of mass m is constrained to move on the parabola z=-in the plane, a is a constant length, and there is a constant gravitational force acting in the negative z direction. (a) [3 points] write the lagrangian using as the generalized coordinate of the particle. (b) [2 points] write the equation of motion from the lagrangian? (c) [3 points] write the equation for small oscillations about the equilibrium point. (d) [2 points] what is the angular frequency for the small oscillations in (c)?