A uniform beam, simply supported at both ends, is found to vibrate in its first mode with an amplitude of \(10 \mathrm{~mm}\) at its center. If \(A=120 \mathrm{~mm}^{2}, I=1000 \mathrm{~mm}^{4}, E=20.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}\), \(ho=7.83 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), and \(l=1 \mathrm{~m}\), determine the maximum bending moment in the beam.