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.
An 80 kg mass is supported by a spring with a stiffness of 100 kN/m and a viscous damper with a damping coefficient of 450 N·s/m. Find the damping ratio ζ.
A 10 kg mass is supported by a spring with a stiffness of 2 kN/m and a viscous damper with a damping coefficient of 70 N·s/m. Find the damping ratio ζ.
A 50 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 15 kN/m and the lower one k₂ = 40 kN/m. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.
A 25 kg mass hangs from spring k₃ = 25 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 12 kN/m and k₂ = 10 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.