Mechanical vibrations worksheet with answers

Free printable Mechanical vibrations worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
k = 50 kN/mm = 150 kgx

A 150 kg mass hangs from a spring with a stiffness of 50 kN/m. Ignore damping. Find the natural frequency fn in Hz.

m = 150 kgk = 50 kN/m
fn = Hz
2.Easy
k = 150 kN/mm = 150 kgx

A 150 kg mass hangs from a spring with a stiffness of 150 kN/m. Ignore damping. Find the natural frequency fn in Hz.

m = 150 kgk = 150 kN/m
fn = Hz
3.Medium
k = 1 kN/mζ = 0.35m = 10 kg

A 10 kg mass on a spring with a stiffness of 1 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.

m = 10 kgk = 1 kN/mζ = 0.35
fd = Hz
4.Medium
k = 40 kN/mζ = 0.6m = 100 kg

A 100 kg mass on a spring with a stiffness of 40 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.

m = 100 kgk = 40 kN/mζ = 0.6
fd = Hz
5.Hard
k1​ = 12k2​ = 60k3​ = 5m = 50 kg

A 50 kg mass hangs from spring k₃ = 5 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 = 60 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.

m = 50 kgk1 = 12 kN/mk2 = 60 kN/mk3 = 5 kN/m
fn = Hz
6.Hard
k1​ = 15k2​ = 40k3​ = 80m = 5 kg

A 5 kg mass hangs from spring k₃ = 80 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 15 kN/m and k₂ = 40 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.

m = 5 kgk1 = 15 kN/mk2 = 40 kN/mk3 = 80 kN/m
fn = Hz

Answer key

  1. 1. fn = 2.906 Hz
  2. 2. fn = 5.033 Hz
  3. 3. fd = 1.491 Hz
  4. 4. fd = 2.546 Hz
  5. 5. fn = 1.539 Hz
  6. 6. fn = 12.85 Hz

Full step-by-step solutions: practise this topic on examproblems.com.