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

m = 5 kgk = 40 kN/m

f_n = Hz

2.Easy

A 500 kg mass hangs from a spring with a stiffness of 100 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 500 kgk = 100 kN/m

f_n = Hz

3.Medium

A 40 kg mass is supported by a spring with a stiffness of 100 kN/m and a viscous damper with a damping coefficient of 600 N·s/m. Find the damping ratio ζ.

m = 40 kgk = 100 kN/mc = 600 N·s/m

ζ =

4.Medium

An 8 kg mass is supported by a spring with a stiffness of 5 kN/m and a viscous damper with a damping coefficient of 80 N·s/m. Find the damping ratio ζ.

m = 8 kgk = 5 kN/mc = 80 N·s/m

ζ =

5.Hard

A 25 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 50 kN/m and k₂ = 5 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 25 kgk₁ = 50 kN/mk₂ = 5 kN/m

k_eq = kN/m

6.Hard

A 100 kg mass hangs from spring k₃ = 15 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 = 30 kN/m; the bar stays level. Ignore damping and the masses of the springs and bar. Find the natural frequency f_n of vertical vibration in Hz.

m = 100 kgk₁ = 25 kN/mk₂ = 30 kN/mk₃ = 15 kN/m

f_n = Hz

Answer key

1. f_n = 14.24 Hz
2. f_n = 2.251 Hz
3. ζ = 0.15
4. ζ = 0.2
5. k_eq = 55 kN/m
6. f_n = 1.728 Hz

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