(Solved): Problem 1: Consider the system below, which consists of springs and masses. Spring stiffnesses are ...

Problem 1: Consider the system below, which consists of springs and masses. Spring stiffnesses are given. Forces \( F_{1} \) and \( F_{2} \) are applied, resulting in displacements \( u_{1} \) and \( u_{2} \). Rotation is restrained. Using the principle of stationary potential energy, derive the equilibrium equations for the system and express them in the form \( [k]\{u\}=\{F\} \).