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

m = 200 kgk = 150 kN/m

f_n = Hz

2.Easy

A 5 kg mass hangs from a spring with a stiffness of 15 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 5 kgk = 15 kN/m

ω_n = rad/s

3.Medium

A 10 kg mass is supported by a spring with a stiffness of 25 kN/m and a viscous damper with a damping coefficient of 300 N·s/m. Find the damping ratio ζ.

m = 10 kgk = 25 kN/mc = 300 N·s/m

ζ =

4.Medium

A 40 kg mass on a spring with a stiffness of 200 kN/m has a viscous damper giving a damping ratio of 0.7. Find the damped natural frequency f_d of its free vibration in Hz.

m = 40 kgk = 200 kN/mζ = 0.7

f_d = Hz

5.Hard

A 50 kg mass hangs from spring k₃ = 20 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 10 kN/m and k₂ = 5 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 = 50 kgk₁ = 10 kN/mk₂ = 5 kN/mk₃ = 20 kN/m

f_n = Hz

6.Hard

A 25 kg mass hangs from two springs connected end to end (in series): the upper spring has k₁ = 40 kN/m and the lower one k₂ = 50 kN/m. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 25 kgk₁ = 40 kN/mk₂ = 50 kN/m

k_eq = kN/m

Answer key

1. f_n = 4.359 Hz
2. ω_n = 54.77 rad/s
3. ζ = 0.3
4. f_d = 8.037 Hz
5. f_n = 2.084 Hz
6. k_eq = 22.22 kN/m

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