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

m = 10 kgk = 80 kN/m

f_n = Hz

2.Easy

A 15 kg mass hangs from a spring with a stiffness of 40 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 15 kgk = 40 kN/m

f_n = Hz

3.Medium

A 50 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 f_d of its free vibration in Hz.

m = 50 kgk = 25 kN/mζ = 0.35

f_d = Hz

4.Medium

In a free-vibration test of a damped mass–spring system, a displacement peak of 25 mm is followed one cycle later by a peak of 13.3 mm. Find the damping ratio ζ.

x₀ = 25 mmx₁ = 13.3 mmn = 1

ζ =

5.Hard

A 5 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 50 kN/m and k₂ = 50 kN/m. The mass stays level. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 5 kgk₁ = 50 kN/mk₂ = 50 kN/m

f_n = Hz

6.Hard

A 20 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 50 kN/m and k₂ = 40 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 20 kgk₁ = 50 kN/mk₂ = 40 kN/m

k_eq = kN/m

Answer key

1. f_n = 14.24 Hz
2. f_n = 8.219 Hz
3. f_d = 3.334 Hz
4. ζ = 0.09994
5. f_n = 22.51 Hz
6. k_eq = 90 kN/m

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