A machine rests on spring mounts, which compress by 8 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 100 kN/m. Ignore damping. Find the natural circular frequency ωn in rad/s.
A 2 kg mass on a spring with a stiffness of 15 kN/m has a viscous damper giving a damping ratio of 0.6. Find the damped natural frequency fd of its free vibration in Hz.
A 2 kg mass on a spring with a stiffness of 25 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 = 60 kN/m and the lower one k₂ = 12 kN/m. Find the equivalent stiffness keq of the spring system in kN/m.
A 100 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 25 kN/m and the lower one k₂ = 50 kN/m. Find the equivalent stiffness keq of the spring system in kN/m.
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