Question 4: Figure 1 shows a block foundation of mass 200 kg supported by two springs of stiffness k = 60 kN/m and a viscous vibration damper with damping coefficient c = 1000 Nm/s. The foundation carries a 40 kg rotating machine which induced 50 N harmonic forced. The foundation block was observed to vibrate badly at frequency of 204 rpm. Explain why the foundation block experienced high vibration phenomena and suggest a solution to reduce half of its vibration amplitude.

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A: m = 3.6 kg c = 513 Ns/m k = 24 kN/m = 24000 N/m

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.