A machine rests on spring mounts, which compress by 0.5 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 2 kN/m. Ignore damping. Find the natural frequency fn in Hz.
In a free-vibration test of a damped mass–spring system, a displacement peak of 12 mm is followed one cycle later by a peak of 6.4 mm. Find the damping ratio ζ.
A 20 kg mass is supported by a spring with a stiffness of 4 kN/m and a viscous damper with a damping coefficient of 340 N·s/m. Find the damping ratio ζ.
A 10 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 12 kN/m and k₂ = 40 kN/m. The mass stays level. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.
A 100 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 50 kN/m and k₂ = 15 kN/m. The mass stays level. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.
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