A machine with a mass of \(50 \mathrm{~kg}\) is mounted on springs of equivalent stiffness \(6.10 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and subject to a harmonic force of \(370 \sin 35 t \mathrm{~N}\) while operating. The natural frequency is close enough to the excitation frequency for beating to occur.

(a) Write the overall response of the system, including the free response.

(b) Plot the response of the system.

(c) What is the maximum amplitude?

(d) What is the period of beating?