Consider the system shown in Figure P1.12a, where (m=10 mathrm{~kg}), (ell_{1}=35 mathrm{~cm}), and (ell=50 mathrm{~cm}). A record

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Consider the system shown in Figure P1.12a, where \(m=10 \mathrm{~kg}\), \(\ell_{1}=35 \mathrm{~cm}\), and \(\ell=50 \mathrm{~cm}\).

A record of free vibration is shown in Figure 1.12b. Find the values of the spring constant \(k\) and the damping coefficient \(c\).

Figure P1.12(a,b)

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