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

m = 50 kgk = 8 kN/m

f_n = Hz

2.Easy

A 25 kg mass hangs from a spring with a stiffness of 5 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 25 kgk = 5 kN/m

f_n = Hz

3.Medium

A 12 kg mass on a spring with a stiffness of 80 kN/m has a viscous damper giving a damping ratio of 0.45. Find the damped natural frequency f_d of its free vibration in Hz.

m = 12 kgk = 80 kN/mζ = 0.45

f_d = Hz

4.Medium

A 500 kg mass on a spring with a stiffness of 80 kN/m has a viscous damper giving a damping ratio of 0.5. Find the damped natural frequency f_d of its free vibration in Hz.

m = 500 kgk = 80 kN/mζ = 0.5

f_d = Hz

5.Hard

A 100 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 15 kN/m and k₂ = 100 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 = 100 kgk₁ = 15 kN/mk₂ = 100 kN/m

f_n = Hz

6.Hard

A 25 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 12 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 = 12 kN/mk₂ = 5 kN/m

f_n = Hz

Answer key

1. f_n = 2.013 Hz
2. f_n = 2.251 Hz
3. f_d = 11.6 Hz
4. f_d = 1.743 Hz
5. f_n = 5.397 Hz
6. f_n = 4.15 Hz

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