The model structure shown in Figure Q1 comprises two iden- tical rigid links each of length L with a pin joint connecting them. The bottom end of the structure has a rotational spring of stiffness K as shown. The model is loaded by a conservative vertical force of magnitude P at the top roller support as indicated. The structure has an initial imperfection, which is the inclination of the bottom link with respect to the vertical when the spring is unstressed. The single degree of freedom the structure is denoted by the angle of the bottom link from verticality. P K L L Figure Q1: Two-link model structure. (a) Firstly, consider the perfect case i.e. when = 0. Use the total potential energy approach to find all equilibrium paths and determine their stability including that of any critical points that you may identify.