Problem Statement

Every mechanical system can be modeled by an inertia$-$spring$-$dashpot system. The inertia element represents the total mass of the system. The spring shows how elastic the system is$.$ The dashpot reveals the energy loss mechanism in the system $($for example due to friction$).$

The boom $\backslash ($ A B $\backslash )$ of the crane shown in Fig. $1$ is a uniform steel bar of length $10$ m and area of cross section $2500\backslash (\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$ A weight $\backslash ($ W $\backslash )$ is suspended while the crane is stationary. The cable $\backslash ($ C D E B F $\backslash )$ is made of steel and has a crosssectional area of $\backslash (100\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ).$ Neglecting the effect of the cable $\backslash ($ C D E B $\backslash ).$

Suppose the system has no mechanism for loosing energy $($no dashpot or $\backslash ($ c$=0\backslash )).$

a$)$ find the equivalent spring constant of the system in the vertical direction.