Determine the amplitudes of motion of the three masses in Fig. 6.40 when a harmonic force \(F(t)=F_{0} \sin \omega t\) is applied to the lower left mass with \(m=1 \mathrm{~kg}, k=1000 \mathrm{~N} / \mathrm{m}, F_{0}=5 \mathrm{~N}\), and \(\omega=10 \mathrm{rad} / \mathrm{s}\) using the mode superposition method.

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000 k 2m k 000 m m F(t) FIGURE 6.40 Forced motion of a three mass-spring system.