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 = 20 kN/mm = 200 kgx

A 200 kg mass hangs from a spring with a stiffness of 20 kN/m. Ignore damping. Find the natural frequency fn in Hz.

m = 200 kgk = 20 kN/m
fn = Hz
2.Easy
k = 50 kN/mm = 100 kgx

A 100 kg mass hangs from a spring with a stiffness of 50 kN/m. Ignore damping. Find the natural frequency fn in Hz.

m = 100 kgk = 50 kN/m
fn = Hz
3.Medium
k = 4 kN/mζ = 0.7m = 10 kg

A 10 kg mass on a spring with a stiffness of 4 kN/m has a viscous damper giving a damping ratio of 0.7. Find the damped natural frequency fd of its free vibration in Hz.

m = 10 kgk = 4 kN/mζ = 0.7
fd = Hz
4.Medium
k = 20 kN/mζ = 0.5m = 50 kg

A 50 kg mass on a spring with a stiffness of 20 kN/m has a viscous damper giving a damping ratio of 0.5. Find the damped natural frequency fd of its free vibration in Hz.

m = 50 kgk = 20 kN/mζ = 0.5
fd = Hz
5.Hard
k1​ = 30k2​ = 80m = 100 kg

A 100 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 30 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.

m = 100 kgk1 = 30 kN/mk2 = 80 kN/m
fn = Hz
6.Hard
k1​ = 25k2​ = 25k3​ = 10m = 10 kg

A 10 kg mass hangs from spring k₃ = 10 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 25 kN/m and k₂ = 25 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 = 10 kgk1 = 25 kN/mk2 = 25 kN/mk3 = 10 kN/m
fn = Hz

Answer key

  1. 1. fn = 1.592 Hz
  2. 2. fn = 3.559 Hz
  3. 3. fd = 2.273 Hz
  4. 4. fd = 2.757 Hz
  5. 5. fn = 5.279 Hz
  6. 6. fn = 4.594 Hz

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