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

m = 5 kgk = 10 kN/m

ω_n = rad/s

2.Easy

A 500 kg mass hangs from a spring with a stiffness of 50 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 500 kgk = 50 kN/m

f_n = Hz

3.Medium

A 40 kg mass is supported by a spring with a stiffness of 40 kN/m and a viscous damper with a damping coefficient of 130 N·s/m. Find the damping ratio ζ.

m = 40 kgk = 40 kN/mc = 130 N·s/m

ζ =

4.Medium

A 40 kg mass is supported by a spring with a stiffness of 15 kN/m and a viscous damper with a damping coefficient of 930 N·s/m. Find the damping ratio ζ.

m = 40 kgk = 15 kN/mc = 930 N·s/m

ζ =

5.Hard

A 25 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 25 kN/m and k₂ = 30 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 = 25 kN/mk₂ = 30 kN/m

f_n = Hz

6.Hard

A 5 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 10 kN/m and k₂ = 50 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 = 5 kgk₁ = 10 kN/mk₂ = 50 kN/m

f_n = Hz

Answer key

1. ω_n = 44.72 rad/s
2. f_n = 1.592 Hz
3. ζ = 0.05139
4. ζ = 0.6003
5. f_n = 7.465 Hz
6. f_n = 17.43 Hz

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