A rigid platform with a weight $W$ is held by four columns that have hinged connections at the top and the bottom. The system is braced laterally on each side by two diagonal steel wires as shown. Each diagonal wire, having a cross$-$sectional area A and elastic modulus $E,$ is pretensioned to a high stress. If the masses of the columns and wires are neglected, obtain the differential equations of motion for free vibration

a$)$ in the $x-$direction $($in terms of $u_x),$