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 2 kg mass hangs from a spring with a stiffness of 12 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 2 kgk = 12 kN/m

f_n = Hz

2.Easy

A 20 kg mass hangs from a spring with a stiffness of 2 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 20 kgk = 2 kN/m

f_n = Hz

3.Medium

A 5 kg mass on a spring with a stiffness of 15 kN/m has a viscous damper giving a damping ratio of 0.6. Find the damped natural frequency f_d of its free vibration in Hz.

m = 5 kgk = 15 kN/mζ = 0.6

f_d = Hz

4.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 3290 N·s/m. Find the damping ratio ζ.

m = 150 kgk = 50 kN/mc = 3290 N·s/m

ζ =

5.Hard

A 25 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 5 kN/m and k₂ = 5 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 = 25 kgk₁ = 5 kN/mk₂ = 5 kN/m

f_n = Hz

6.Hard

A 20 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 = 100 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 20 kgk₁ = 20 kN/mk₂ = 100 kN/m

f_n = Hz

Answer key

1. f_n = 12.33 Hz
2. f_n = 1.592 Hz
3. f_d = 6.974 Hz
4. ζ = 0.6007
5. f_n = 3.183 Hz
6. f_n = 4.594 Hz

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