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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A 40 kg mass hangs from a spring with a stiffness of 200 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 40 kgk = 200 kN/m

f_n = Hz

2.Easy

An 80 kg mass hangs from a spring with a stiffness of 40 kN/m. Ignore damping. Find the natural frequency f_n in Hz.

m = 80 kgk = 40 kN/m

f_n = Hz

3.Medium

A 100 kg mass is supported by a spring with a stiffness of 15 kN/m and a viscous damper with a damping coefficient of 1220 N·s/m. Find the damping ratio ζ.

m = 100 kgk = 15 kN/mc = 1220 N·s/m

ζ =

4.Medium

A 25 kg mass on a spring with a stiffness of 8 kN/m has a viscous damper giving a damping ratio of 0.35. Find the damped natural frequency f_d of its free vibration in Hz.

m = 25 kgk = 8 kN/mζ = 0.35

f_d = Hz

5.Hard

A 50 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 12 kN/m and k₂ = 100 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 50 kgk₁ = 12 kN/mk₂ = 100 kN/m

k_eq = kN/m

6.Hard

A 5 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 100 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 = 5 kgk₁ = 100 kN/mk₂ = 30 kN/m

f_n = Hz

Answer key

1. f_n = 11.25 Hz
2. f_n = 3.559 Hz
3. ζ = 0.4981
4. f_d = 2.667 Hz
5. k_eq = 112 kN/m
6. f_n = 25.66 Hz

Full step-by-step solutions: practise this topic on examproblems.com.