On this webpage you will find my solutions to the fifth edition of "Theory of Vibration with Applications" by William Thomson and Marie Dahleh. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.

Chapter 1: Oscillatory Motion
Problem 1 Problem 6 Problem 11 Problem 16 Problem 21
Problem 2 Problem 7 Problem 12 Problem 17 Problem 22
Problem 3 Problem 8 Problem 13 Problem 18 Problem 23
Problem 4 Problem 9 Problem 14 Problem 19 Problem 24
Problem 5 Problem 10 Problem 15 Problem 20 Problem 25
Chapter 2: Free Vibration
Problem 1 Problem 14 | Solution Problem 27 | Solution Problem 40 | Solution Problem 53 | Solution
Problem 2 Problem 15 | Solution Problem 28 | Solution Problem 41 | Solution Problem 54 | Solution
Problem 3 Problem 16 | Solution Problem 29 | Solution Problem 42 | Solution Problem 55 | Solution
Problem 4 Problem 17 | Solution Problem 30 | Solution Problem 43 | Solution Problem 56 | Solution
Problem 5 Problem 18 | Solution Problem 31 | Solution Problem 44 | Solution Problem 57 | Solution
Problem 6 Problem 19 | Solution Problem 32 | Solution Problem 45 | Solution Problem 58 | Solution
Problem 7 Problem 20 | Solution Problem 33 | Solution Problem 46 | Solution Problem 59 | Solution
Problem 8 Problem 21 | Solution Problem 34 | Solution Problem 47 | Solution Problem 60 | Solution
Problem 9 | Solution Problem 22 | Solution Problem 35 | Solution Problem 48 | Solution Problem 61 | Solution
Problem 10 | Solution Problem 23 | Solution Problem 36 | Solution Problem 49 | Solution Problem 62 | Solution
Problem 11 | Solution Problem 24 | Solution Problem 37 | Solution Problem 50 | Solution
Problem 12 | Solution Problem 25 | Solution Problem 38 | Solution Problem 51 | Solution
Problem 13 | Solution Problem 26 | Solution Problem 39 | Solution Problem 52 | Solution
Chapter 3: Harmonically Excited Vibration
Problem 1 | Solution Problem 14 | Solution Problem 27 | Solution Problem 40 | Solution Problem 53 | Solution
Problem 2 | Solution Problem 15 | Solution Problem 28 | Solution Problem 41 | Solution Problem 54 | Solution
Problem 3 | Solution Problem 16 | Solution Problem 29 | Solution Problem 42 | Solution Problem 55 | Solution
Problem 4 | Solution Problem 17 | Solution Problem 30 | Solution Problem 43 | Solution Problem 56 | Solution
Problem 5 | Solution Problem 18 | Solution Problem 31 | Solution Problem 44 | Solution Problem 57 | Solution
Problem 6 | Solution Problem 19 | Solution Problem 32 | Solution Problem 45 | Solution Problem 58 | Solution
Problem 7 | Solution Problem 20 | Solution Problem 33 | Solution Problem 46 | Solution Problem 59 | Solution
Problem 8 | Solution Problem 21 | Solution Problem 34 | Solution Problem 47 | Solution Problem 60 | Solution
Problem 9 | Solution Problem 22 | Solution Problem 35 | Solution Problem 48 | Solution Problem 61 | Solution
Problem 10 | Solution Problem 23 | Solution Problem 36 | Solution Problem 49 | Solution Problem 62 | Solution
Problem 11 | Solution Problem 24 | Solution Problem 37 | Solution Problem 50 | Solution
Problem 12 | Solution Problem 25 | Solution Problem 38 | Solution Problem 51 | Solution
Problem 13 | Solution Problem 26 | Solution Problem 39 | Solution Problem 52 | Solution
Chapter 4: Transient Vibration
Problem 1 | Solution Problem 11 | Solution Problem 21 | Solution Problem 31 | Solution Problem 41 | Solution
Problem 2 | Solution Problem 12 | Solution Problem 22 | Solution Problem 32 | Solution Problem 42 | Solution
Problem 3 | Solution Problem 13 | Solution Problem 23 | Solution Problem 33 | Solution Problem 43 | Solution
Problem 4 | Solution Problem 14 | Solution Problem 24 | Solution Problem 34 | Solution Problem 44 | Solution
Problem 5 | Solution Problem 15 | Solution Problem 25 | Solution Problem 35 | Solution Problem 45 | Solution
Problem 6 | Solution Problem 16 | Solution Problem 26 | Solution Problem 36 | Solution Problem 46 | Solution
Problem 7 | Solution Problem 17 | Solution Problem 27 | Solution Problem 37 | Solution Problem 47 | Solution
Problem 8 | Solution Problem 18 | Solution Problem 28 | Solution Problem 38 | Solution Problem 48 | Solution
Problem 9 | Solution Problem 19 | Solution Problem 29 | Solution Problem 39 | Solution
Problem 10 | Solution Problem 20 | Solution Problem 30 | Solution Problem 40 | Solution
Chapter 5: Systems With Two or More Degrees of Freedom
Problem 1 | Solution Problem 14 | Solution Problem 27 | Solution Problem 40 | Solution Problem 53 | Solution
Problem 2 | Solution Problem 15 | Solution Problem 28 | Solution Problem 41 | Solution Problem 54 | Solution
Problem 3 | Solution Problem 16 | Solution Problem 29 | Solution Problem 42 | Solution Problem 55 | Solution
Problem 4 | Solution Problem 17 | Solution Problem 30 | Solution Problem 43 | Solution Problem 56 | Solution
Problem 5 | Solution Problem 18 | Solution Problem 31 | Solution Problem 44 | Solution Problem 57 | Solution
Problem 6 | Solution Problem 19 | Solution Problem 32 | Solution Problem 45 | Solution Problem 58 | Solution
Problem 7 | Solution Problem 20 | Solution Problem 33 | Solution Problem 46 | Solution Problem 59 | Solution
Problem 8 | Solution Problem 21 | Solution Problem 34 | Solution Problem 47 | Solution Problem 60 | Solution
Problem 9 | Solution Problem 22 | Solution Problem 35 | Solution Problem 48 | Solution Problem 61 | Solution
Problem 10 | Solution Problem 23 | Solution Problem 36 | Solution Problem 49 | Solution Problem 62 | Solution
Problem 11 | Solution Problem 24 | Solution Problem 37 | Solution Problem 50 | Solution Problem 63 | Solution
Problem 12 | Solution Problem 25 | Solution Problem 38 | Solution Problem 51 | Solution Problem 64 | Solution
Problem 13 | Solution Problem 26 | Solution Problem 39 | Solution Problem 52 | Solution Problem 65 | Solution
Chapter 6: Properties of Vibrating Systems
Problem 1 | Solution Problem 10 | Solution Problem 19 | Solution Problem 28 | Solution Problem 37 | Solution
Problem 2 | Solution Problem 11 | Solution Problem 20 | Solution Problem 29 | Solution Problem 38 | Solution
Problem 3 | Solution Problem 12 | Solution Problem 21 | Solution Problem 30 | Solution Problem 39 | Solution
Problem 4 | Solution Problem 13 | Solution Problem 22 | Solution Problem 31 | Solution Problem 40 | Solution
Problem 5 | Solution Problem 14 | Solution Problem 23 | Solution Problem 32 | Solution Problem 41 | Solution
Problem 6 | Solution Problem 15 | Solution Problem 24 | Solution Problem 33 | Solution Problem 42 | Solution
Problem 7 | Solution Problem 16 | Solution Problem 25 | Solution Problem 34 | Solution Problem 43 | Solution
Problem 8 | Solution Problem 17 | Solution Problem 26 | Solution Problem 35 | Solution Problem 44 | Solution
Problem 9 | Solution Problem 18 | Solution Problem 27 | Solution Problem 36 | Solution Problem 45 | Solution
Chapter 7: Lagrange's Equation
Problem 1 | Solution Problem 7 | Solution Problem 13 | Solution Problem 19 | Solution Problem 25 | Solution
Problem 2 | Solution Problem 8 | Solution Problem 14 | Solution Problem 20 | Solution Problem 26 | Solution
Problem 3 | Solution Problem 9 | Solution Problem 15 | Solution Problem 21 | Solution Problem 27 | Solution
Problem 4 | Solution Problem 10 | Solution Problem 16 | Solution Problem 22 | Solution
Problem 5 | Solution Problem 11 | Solution Problem 17 | Solution Problem 23 | Solution
Problem 6 | Solution Problem 12 | Solution Problem 18 | Solution Problem 24 | Solution
Chapter 8: Computational Methods
Problem 1 | Solution Problem 7 | Solution Problem 13 | Solution Problem 19 | Solution Problem 25 | Solution
Problem 2 | Solution Problem 8 | Solution Problem 14 | Solution Problem 20 | Solution Problem 26 | Solution
Problem 3 | Solution Problem 9 | Solution Problem 15 | Solution Problem 21 | Solution Problem 27 | Solution
Problem 4 | Solution Problem 10 | Solution Problem 16 | Solution Problem 22 | Solution
Problem 5 | Solution Problem 11 | Solution Problem 17 | Solution Problem 23 | Solution
Problem 6 | Solution Problem 12 | Solution Problem 18 | Solution Problem 24 | Solution
Chapter 9: Vibration of Continuous Systems
Problem 1 | Solution Problem 10 | Solution Problem 19 | Solution Problem 28 | Solution Problem 37 | Solution
Problem 2 | Solution Problem 11 | Solution Problem 20 | Solution Problem 29 | Solution Problem 38 | Solution
Problem 3 | Solution Problem 12 | Solution Problem 21 | Solution Problem 30 | Solution Problem 39 | Solution
Problem 4 | Solution Problem 13 | Solution Problem 22 | Solution Problem 31 | Solution Problem 40 | Solution
Problem 5 | Solution Problem 14 | Solution Problem 23 | Solution Problem 32 | Solution Problem 41 | Solution
Problem 6 | Solution Problem 15 | Solution Problem 24 | Solution Problem 33 | Solution Problem 42 | Solution
Problem 7 | Solution Problem 16 | Solution Problem 25 | Solution Problem 34 | Solution
Problem 8 | Solution Problem 17 | Solution Problem 26 | Solution Problem 35 | Solution
Problem 9 | Solution Problem 18 | Solution Problem 27 | Solution Problem 36 | Solution
Chapter 10: Introduction to the Finite Element Method
Problem 1 | Solution Problem 10 | Solution Problem 19 | Solution Problem 28 | Solution Problem 37 | Solution
Problem 2 | Solution Problem 11 | Solution Problem 20 | Solution Problem 29 | Solution Problem 38 | Solution
Problem 3 | Solution Problem 12 | Solution Problem 21 | Solution Problem 30 | Solution Problem 39 | Solution
Problem 4 | Solution Problem 13 | Solution Problem 22 | Solution Problem 31 | Solution Problem 40 | Solution
Problem 5 | Solution Problem 14 | Solution Problem 23 | Solution Problem 32 | Solution Problem 41 | Solution
Problem 6 | Solution Problem 15 | Solution Problem 24 | Solution Problem 33 | Solution Problem 42 | Solution
Problem 7 | Solution Problem 16 | Solution Problem 25 | Solution Problem 34 | Solution Problem 43 | Solution
Problem 8 | Solution Problem 17 | Solution Problem 26 | Solution Problem 35 | Solution
Problem 9 | Solution Problem 18 | Solution Problem 27 | Solution Problem 36 | Solution
Chapter 11: Mode-Summation Procedures for Continuous Systems
Problem 1 | Solution Problem 6 | Solution Problem 11 | Solution Problem 16 | Solution Problem 21 | Solution
Problem 2 | Solution Problem 7 | Solution Problem 12 | Solution Problem 17 | Solution Problem 22 | Solution
Problem 3 | Solution Problem 8 | Solution Problem 13 | Solution Problem 18 | Solution Problem 23 | Solution
Problem 4 | Solution Problem 9 | Solution Problem 14 | Solution Problem 19 | Solution Problem 24 | Solution
Problem 5 | Solution Problem 10 | Solution Problem 15 | Solution Problem 20 | Solution Problem 25 | Solution
Chapter 12: Classical Methods
Problem 1 | Solution Problem 11 | Solution Problem 21 | Solution Problem 31 | Solution Problem 41 | Solution
Problem 2 | Solution Problem 12 | Solution Problem 22 | Solution Problem 32 | Solution Problem 42 | Solution
Problem 3 | Solution Problem 13 | Solution Problem 23 | Solution Problem 33 | Solution Problem 43 | Solution
Problem 4 | Solution Problem 14 | Solution Problem 24 | Solution Problem 34 | Solution Problem 44 | Solution
Problem 5 | Solution Problem 15 | Solution Problem 25 | Solution Problem 35 | Solution Problem 45 | Solution
Problem 6 | Solution Problem 16 | Solution Problem 26 | Solution Problem 36 | Solution Problem 46 | Solution
Problem 7 | Solution Problem 17 | Solution Problem 27 | Solution Problem 37 | Solution Problem 47 | Solution
Problem 8 | Solution Problem 18 | Solution Problem 28 | Solution Problem 38 | Solution Problem 48 | Solution
Problem 9 | Solution Problem 19 | Solution Problem 29 | Solution Problem 39 | Solution Problem 49 | Solution
Problem 10 | Solution Problem 20 | Solution Problem 30 | Solution Problem 40 | Solution Problem 50 | Solution
Chapter 13: Random Vibrations
Problem 1 | Solution Problem 12 | Solution Problem 23 | Solution Problem 34 | Solution Problem 45 | Solution
Problem 2 | Solution Problem 13 | Solution Problem 24 | Solution Problem 35 | Solution Problem 46 | Solution
Problem 3 | Solution Problem 14 | Solution Problem 25 | Solution Problem 36 | Solution Problem 47 | Solution
Problem 4 | Solution Problem 15 | Solution Problem 26 | Solution Problem 37 | Solution Problem 48 | Solution
Problem 5 | Solution Problem 16 | Solution Problem 27 | Solution Problem 38 | Solution Problem 49 | Solution
Problem 6 | Solution Problem 17 | Solution Problem 28 | Solution Problem 39 | Solution Problem 50 | Solution
Problem 7 | Solution Problem 18 | Solution Problem 29 | Solution Problem 40 | Solution Problem 51 | Solution
Problem 8 | Solution Problem 19 | Solution Problem 30 | Solution Problem 41 | Solution
Problem 9 | Solution Problem 20 | Solution Problem 31 | Solution Problem 42 | Solution
Problem 10 | Solution Problem 21 | Solution Problem 32 | Solution Problem 43 | Solution
Problem 11 | Solution Problem 22 | Solution Problem 33 | Solution Problem 44 | Solution
Chapter 14: Nonlinear Vibrations
Problem 1 | Solution Problem 10 | Solution Problem 19 | Solution Problem 28 | Solution Problem 37 | Solution
Problem 2 | Solution Problem 11 | Solution Problem 20 | Solution Problem 29 | Solution Problem 38 | Solution
Problem 3 | Solution Problem 12 | Solution Problem 21 | Solution Problem 30 | Solution Problem 39 | Solution
Problem 4 | Solution Problem 13 | Solution Problem 22 | Solution Problem 31 | Solution Problem 40 | Solution
Problem 5 | Solution Problem 14 | Solution Problem 23 | Solution Problem 32 | Solution Problem 41 | Solution
Problem 6 | Solution Problem 15 | Solution Problem 24 | Solution Problem 33 | Solution Problem 42 | Solution
Problem 7 | Solution Problem 16 | Solution Problem 25 | Solution Problem 34 | Solution Problem 43 | Solution
Problem 8 | Solution Problem 17 | Solution Problem 26 | Solution Problem 35 | Solution Problem 44 | Solution
Problem 9 | Solution Problem 18 | Solution Problem 27 | Solution Problem 36 | Solution Problem 45 | Solution