A uniform slender rod of mass \(m\) and length \(l\) is hinged at point \(A\) and is attached to four linear springs and one torsional spring, as shown in Fig. 2.102. Find the natural frequency of the system if \(k=2000 \mathrm{~N} / \mathrm{m}, k_{t}=1000 \mathrm{~N}-\mathrm{m} / \mathrm{rad}, m=10 \mathrm{~kg}\), and \(l=5 \mathrm{~m}\).

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1 k 000 k 000 A k 3. 000 k 000 21 3 FIGURE 2.102 Slender rod connected to springs.