The mechanism shown in the figure consists of two links. Each link is a uniform rod with a mass of m=2 kg. The length of each rod is L=300 mm. O is attached to the inertial frame through a frictionless revolute joint. A is a frictionless revolute joint between the two rods. B is constrained to move horizontally in a frictionless slot. B is horizontally in line with O. A spring of stiffness k joins the centres of the two rods. The system is released from rest with an angle 0=60 between the horizontal and rod OA. In this position, the spring is unstressed. It comes momentarily to rest at a lowest position where 0=30. Gravity, g=9.81 m/s?, acts vertically downwards. 1. Calculate the stiffness, k, of the spring. 2. Calculate the horizontal velocity of B when 0=45 3. Use Lagrange's equation to derive the differential equation of motion in terms of the coordinate 0. A B O