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

m = 2 kgk = 8 kN/m

ω_n = rad/s

2.Easy

An 8 kg mass hangs from a spring with a stiffness of 5 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 8 kgk = 5 kN/m

f_n = Hz

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

An 80 kg mass on a spring with a stiffness of 50 kN/m has a viscous damper giving a damping ratio of 0.4. Find the damped natural frequency f_d of its free vibration in Hz.

m = 80 kgk = 50 kN/mζ = 0.4

f_d = Hz

5.Hard

A 5 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 15 kN/m and k₂ = 12 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 5 kgk₁ = 15 kN/mk₂ = 12 kN/m

k_eq = kN/m

6.Hard

A 40 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 50 kN/m and k₂ = 60 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 = 40 kgk₁ = 50 kN/mk₂ = 60 kN/m

f_n = Hz

Answer key

1. ω_n = 63.25 rad/s
2. f_n = 3.979 Hz
3. f_d = 7.797 Hz
4. f_d = 3.647 Hz
5. k_eq = 27 kN/m
6. f_n = 8.346 Hz

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