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 machine rests on spring mounts, which compress by 4 mm under its weight. Treat it as an undamped single-degree-of-freedom system and use g = 9.81 m/s². Find the natural frequency f_n of vertical vibration in Hz.

δ_st = 4 mmg = 9.81 m/s²

f_n = Hz

2.Easy

A 12 kg mass hangs from a spring with a stiffness of 4 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 12 kgk = 4 kN/m

ω_n = rad/s

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 200 N·s/m. Find the damping ratio ζ.

m = 100 kgk = 15 kN/mc = 200 N·s/m

ζ =

4.Medium

A 10 kg mass on a spring with a stiffness of 12 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 = 10 kgk = 12 kN/mζ = 0.45

f_d = Hz

5.Hard

A 50 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 30 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 = 30 kN/mk₂ = 100 kN/m

k_eq = kN/m

6.Hard

A 20 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 80 kN/m and k₂ = 30 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 20 kgk₁ = 80 kN/mk₂ = 30 kN/m

k_eq = kN/m

Answer key

1. f_n = 7.882 Hz
2. ω_n = 18.26 rad/s
3. ζ = 0.08165
4. f_d = 4.924 Hz
5. k_eq = 130 kN/m
6. k_eq = 110 kN/m

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