The masses of the tup, frame, anvil (along with the workpiece), and foundation block in a forging hammer (Fig. 5.51) are \(2200 \mathrm{~kg}, 22,000 \mathrm{~kg}, 35,000 \mathrm{~kg}\), and 70,000 kg, respectively.

The stiffnesses of the elastic pad placed between the anvil and the foundation block and the isolation placed underneath the foundation (including the elasticity of the soil) are \(1 \mathrm{GN} / \mathrm{m}\) and \(0.5 \mathrm{GN} / \mathrm{m}\), respectively. If the velocity of the tup before it strikes the anvil is \(5 \mathrm{~m} / \mathrm{s}\), find (a) the natural frequencies of the system, and (b) the magnitudes of displacement of the anvil and the foundation block. Assume the coefficient of restitution as 0.5 and damping to be negligible in the system.

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Trailer, mass M 000 k 000 Cylinder, k mass m FIGURE 5.50 Trailer and cylinder.