A rod is made of two uniform sections, as shown in Figure 5.21. The two sections are made of the same material, and the modulus of elasticity of the rod material is \(E\). The areas for the two sections are \(A_{1}\) and \(A_{2}\), respectively. Derive the equivalent spring constant corresponding to a tensile force \(f\) applied at the free end.

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FIGURE 5.21 Problem 11. E, A E, A L L *