A machine rests on spring mounts, which compress by 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.
An 8 kg mass hangs from a spring with a stiffness of 4 kN/m. Ignore damping. Find the natural circular frequency ωn in rad/s.
A 100 kg mass on a spring with a stiffness of 80 kN/m has a viscous damper giving a damping ratio of 0.3. Find the damped natural frequency fd of its free vibration in Hz.
In a free-vibration test of a damped mass–spring system, a displacement peak of 40 mm is followed 5 cycles later by a peak of 11.4 mm. Find the damping ratio ζ.
A 50 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 30 kN/m and k₂ = 10 kN/m. The mass stays level. Find the equivalent stiffness keq of the spring system in kN/m.
A 40 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 20 kN/m and the lower one k₂ = 50 kN/m. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.
Full step-by-step solutions: practise this topic on examproblems.com.