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.
A 5 kg mass hangs from a spring with a stiffness of 25 kN/m. Ignore damping. Find the natural circular frequency ωn in rad/s.
A 5 kg mass is supported by a spring with a stiffness of 10 kN/m and a viscous damper with a damping coefficient of 270 N·s/m. Find the damping ratio ζ.
A 15 kg mass is supported by a spring with a stiffness of 20 kN/m and a viscous damper with a damping coefficient of 660 N·s/m. Find the damping ratio ζ.
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 = 15 kN/m. Find the equivalent stiffness keq of the spring system in kN/m.
A 20 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 40 kN/m and k₂ = 15 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.