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

A 100 kg mass hangs from a spring with a stiffness of 15 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 100 kgk = 15 kN/m

f_n = Hz

2.Easy

A 150 kg mass hangs from a spring with a stiffness of 100 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 150 kgk = 100 kN/m

f_n = Hz

3.Medium

In a free-vibration test of a damped mass–spring system, a displacement peak of 12 mm is followed 3 cycles later by a peak of 4.7 mm. Find the damping ratio ζ.

x₀ = 12 mmx₃ = 4.7 mmn = 3

ζ =

4.Medium

In a free-vibration test of a damped mass–spring system, a displacement peak of 50 mm is followed 5 cycles later by a peak of 7.6 mm. Find the damping ratio ζ.

x₀ = 50 mmx₅ = 7.6 mmn = 5

ζ =

5.Hard

A 25 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 10 kN/m and the lower one k₂ = 40 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 25 kgk₁ = 10 kN/mk₂ = 40 kN/m

f_n = Hz

6.Hard

A 5 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 = 10 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 5 kgk₁ = 20 kN/mk₂ = 10 kN/m

f_n = Hz

Answer key

1. f_n = 1.949 Hz
2. f_n = 4.109 Hz
3. ζ = 0.04967
4. ζ = 0.05986
5. f_n = 2.847 Hz
6. f_n = 5.812 Hz

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