A machine rests on spring mounts, which compress by 12 mm under its weight. Treat it as an undamped single-degree-of-freedom system and use g = 9.81 m/s². Find the natural frequency fn of vertical vibration in Hz.
A 10 kg mass hangs from a spring with a stiffness of 5 kN/m. Ignore damping. Find the natural circular frequency ωn in rad/s.
In a free-vibration test of a damped mass–spring system, a displacement peak of 30 mm is followed 4 cycles later by a peak of 14.1 mm. Find the damping ratio ζ.
In a free-vibration test of a damped mass–spring system, a displacement peak of 12 mm is followed 3 cycles later by a peak of 6.8 mm. Find the damping ratio ζ.
A 100 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 30 kN/m and the lower one k₂ = 40 kN/m. Find the equivalent stiffness keq of the spring system in kN/m.
A 25 kg mass hangs from spring k₃ = 10 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 60 kN/m and k₂ = 5 kN/m; the bar stays level. Ignore damping and the masses of the springs and bar. Find the natural frequency fn of vertical vibration in Hz.
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