An electric pole of circular cross section, with a bending stiffness \(k=5000 \mathrm{~N} / \mathrm{m}\) and a damping ratio \(\zeta=0.05\), carries a transformer of mass \(m=250 \mathrm{~kg}\) as shown in Fig. 4.70. It is subjected to an earthquake that is characterized by a response spectrum given in Fig. 4.18. Find (a) maximum relative displacement of the transformer, (b) maximum shear force in the pole, and (c) maximum bending moment in the pole. Assume the length of pole (height of transformer) as \(l=20 \mathrm{~m}\).

Figure 4.18:-

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Transformer, mass (m) Circular pole; bending stiffness (k) x(t) - y(t) Ground motion FIGURE 4.70 Electric pole with transformer at top.