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.

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1.Easy
k = 150 kN/mm = 80 kgx

An 80 kg mass hangs from a spring with a stiffness of 150 kN/m. Ignore damping. Find the natural frequency fn in Hz.

m = 80 kgk = 150 kN/m
fn = Hz
2.Easy
k = 200 kN/mm = 20 kgx

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

m = 20 kgk = 200 kN/m
fn = Hz
3.Medium
k = 80 kN/mζ = 0.6m = 100 kg

A 100 kg mass on a spring with a stiffness of 80 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 = 80 kN/mζ = 0.6
fd = Hz
4.Medium
k = 50 kN/mζ = 0.3m = 8 kg

An 8 kg mass on a spring with a stiffness of 50 kN/m has a viscous damper giving a damping ratio of 0.3. Find the damped natural frequency fd of its free vibration in Hz.

m = 8 kgk = 50 kN/mζ = 0.3
fd = Hz
5.Hard
k1​ = 50k2​ = 25m = 40 kg

A 40 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 50 kN/m and the lower one k₂ = 25 kN/m. Ignore damping and the masses of the springs. Find the natural frequency fn of vertical vibration in Hz.

m = 40 kgk1 = 50 kN/mk2 = 25 kN/m
fn = Hz
6.Hard
k1​ = 20k2​ = 40m = 10 kg

A 10 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 20 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.

m = 10 kgk1 = 20 kN/mk2 = 40 kN/m
fn = Hz

Answer key

  1. 1. fn = 6.892 Hz
  2. 2. fn = 15.92 Hz
  3. 3. fd = 3.601 Hz
  4. 4. fd = 12 Hz
  5. 5. fn = 3.249 Hz
  6. 6. fn = 5.812 Hz

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