For a vibrating system, \(m=10 \mathrm{~kg}, k=2500 \mathrm{~N} / \mathrm{m}\), and \(c=45 \mathrm{~N}-\mathrm{s} / \mathrm{m}\). A harmonic force of amplitude \(180 \mathrm{~N}\) and frequency \(3.5 \mathrm{~Hz}\) acts on the mass. If the initial displacement and velocity of the mass are \(15 \mathrm{~mm}\) and \(5 \mathrm{~m} / \mathrm{s}\), respectively, find the complete solution representing the motion of the mass.