A machine rests on spring mounts, which compress by 1 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 200 kg mass hangs from a spring with a stiffness of 25 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 10 mm is followed one cycle later by a peak of 6.9 mm. Find the damping ratio ζ.
An 80 kg mass on a spring with a stiffness of 12 kN/m has a viscous damper giving a damping ratio of 0.35. Find the damped natural frequency fd of its free vibration in Hz.
A 5 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 5 kN/m and the lower one k₂ = 60 kN/m. Find the equivalent stiffness keq of the spring system in kN/m.
A 50 kg mass hangs from spring k₃ = 12 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 100 kN/m and k₂ = 80 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.
Full step-by-step solutions: practise this topic on examproblems.com.