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 2 kg mass hangs from a spring with a stiffness of 50 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 2 kgk = 50 kN/m

ω_n = rad/s

2.Easy

A 25 kg mass hangs from a spring with a stiffness of 15 kN/m. Ignore damping. Find the natural circular frequency ω_n in rad/s.

m = 25 kgk = 15 kN/m

ω_n = rad/s

3.Medium

A 12 kg mass is supported by a spring with a stiffness of 150 kN/m and a viscous damper with a damping coefficient of 400 N·s/m. Find the damping ratio ζ.

m = 12 kgk = 150 kN/mc = 400 N·s/m

ζ =

4.Medium

A 50 kg mass is supported by a spring with a stiffness of 80 kN/m and a viscous damper with a damping coefficient of 1200 N·s/m. Find the damping ratio ζ.

m = 50 kgk = 80 kN/mc = 1200 N·s/m

ζ =

5.Hard

A 40 kg mass hangs from spring k₃ = 80 kN/m. The top of k₃ is attached to a rigid bar that hangs from two springs side by side, k₁ = 30 kN/m and k₂ = 40 kN/m; the bar stays level. Ignore damping and the masses of the springs and bar. Find the natural frequency f_n of vertical vibration in Hz.

m = 40 kgk₁ = 30 kN/mk₂ = 40 kN/mk₃ = 80 kN/m

f_n = Hz

6.Hard

A 20 kg mass hangs from two springs side by side (in parallel), with stiffnesses k₁ = 12 kN/m and k₂ = 40 kN/m. The mass stays level. Find the equivalent stiffness k_eq of the spring system in kN/m.

m = 20 kgk₁ = 12 kN/mk₂ = 40 kN/m

k_eq = kN/m

Answer key

1. ω_n = 158.1 rad/s
2. ω_n = 24.49 rad/s
3. ζ = 0.1491
4. ζ = 0.3
5. f_n = 4.862 Hz
6. k_eq = 52 kN/m

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