A (40 mathrm{~kg}) machine is attached to a base through a spring of stiffness (2 times 10^{4}

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A \(40 \mathrm{~kg}\) machine is attached to a base through a spring of stiffness \(2 \times 10^{4} \mathrm{~N} / \mathrm{m}\) in parallel with a dashpot of damping coefficient \(150 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\). The base is given a time-dependent displacement \(0.15 \sin 30.1 \mathrm{t} \mathrm{m}\). Determine the amplitude of the absolute displacement of the machine and the amplitude of displacement of the machine relative to the base.

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