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 8 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 20 kgk = 8 kN/m

ω_n = rad/s

2.Easy

A 25 kg mass hangs from a spring with a stiffness of 25 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 25 kgk = 25 kN/m

ω_n = rad/s

3.Medium

A 40 kg mass on a spring with a stiffness of 150 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 = 40 kgk = 150 kN/mζ = 0.6

f_d = Hz

4.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 1000 N·s/m. Find the damping ratio ζ.

m = 40 kgk = 100 kN/mc = 1000 N·s/m

ζ =

5.Hard

A 20 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 = 50 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 20 kgk₁ = 100 kN/mk₂ = 50 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 = 25 kN/m and the lower one k₂ = 60 kN/m. Ignore damping and the masses of the springs. Find the natural frequency f_n of vertical vibration in Hz.

m = 20 kgk₁ = 25 kN/mk₂ = 60 kN/m

f_n = Hz

Answer key

1. ω_n = 20 rad/s
2. ω_n = 31.62 rad/s
3. f_d = 7.797 Hz
4. ζ = 0.25
5. f_n = 6.497 Hz
6. f_n = 4.728 Hz

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