A 500-kg press is placed at the midspan of a simply supported beam of length \(3 \mathrm{~m}\), elastic modulus \(200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\), and cross-sectional moment of inertia \(1.83 \times 10^{-5} \mathrm{~m}^{4}\). It is observed that free vibrations of the beam decay to half of the initial amplitude in 35 cycles. Determine the response of the press, \(x(t)\), if it is subject to an impulse of magnitude \(10,000 \mathrm{~N} \cdot \mathrm{s}\).