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

m = 20 kgk = 150 kN/m

f_n = Hz

2.Easy

A 15 kg mass hangs from a spring with a stiffness of 10 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 15 kgk = 10 kN/m

ω_n = rad/s

3.Medium

A 150 kg mass is supported by a spring with a stiffness of 50 kN/m and a viscous damper with a damping coefficient of 1100 N·s/m. Find the damping ratio ζ.

m = 150 kgk = 50 kN/mc = 1100 N·s/m

ζ =

4.Medium

A 12 kg mass on a spring with a stiffness of 80 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 = 12 kgk = 80 kN/mζ = 0.35

f_d = Hz

5.Hard

A 50 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 100 kN/m and the lower one k₂ = 20 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 50 kgk₁ = 100 kN/mk₂ = 20 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 = 12 kN/m and the lower one k₂ = 20 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 5 kgk₁ = 12 kN/mk₂ = 20 kN/m

f_n = Hz

Answer key

1. f_n = 13.78 Hz
2. ω_n = 25.82 rad/s
3. ζ = 0.2008
4. f_d = 12.17 Hz
5. f_n = 2.906 Hz
6. f_n = 6.164 Hz

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