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 2 kg mass hangs from a spring with a stiffness of 5 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 50 mm is followed one cycle later by a peak of 41.4 mm. Find the damping ratio ζ.
A 100 kg mass is supported by a spring with a stiffness of 150 kN/m and a viscous damper with a damping coefficient of 4650 N·s/m. Find the damping ratio ζ.
A 100 kg mass hangs from spring k₃ = 50 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 80 kN/m and k₂ = 25 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.
A 40 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 100 kN/m and k₂ = 50 kN/m. The mass stays level. Find the equivalent stiffness keq of the spring system in kN/m.
Full step-by-step solutions: practise this topic on examproblems.com.