Question: 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

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.

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