A machine rests on spring mounts, which compress by 20 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 machine rests on spring mounts, which compress by 15 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 is supported by a spring with a stiffness of 50 kN/m and a viscous damper with a damping coefficient of 50 N·s/m. Find the damping ratio ζ.
A 10 kg mass is supported by a spring with a stiffness of 12 kN/m and a viscous damper with a damping coefficient of 100 N·s/m. Find the damping ratio ζ.
A 5 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 80 kN/m and k₂ = 80 kN/m. The mass stays level. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.
A 10 kg mass hangs from spring k₃ = 100 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 50 kN/m and k₂ = 20 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.