---
title: "Vibration terms, effects and elements"
subject: "Theory of Mechanism and Machine II"
chapter: 6
key: "semester_7/theory_of_mechanism_and_machine_ii:vibration-terms-effects-notes"
source: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/vibration-terms-effects-notes
site: BCT Engineering
---

# Vibration terms, effects and elements

Theory of Mechanism and Machine II · Chapter 6: Vibration of Single Degree of Freedom Systems

- Asked in: year not given, 5 marks
- Video: [TOM-01 Introduction of Vibration I Elementary Parts of Vibrating Systems I Effect of Vibration I MCQ](https://www.youtube.com/watch?v=5QafqRz2AM0) — Manu Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/vibration-terms-effects-notes
- Whole chapter: https://www.bctengineer.com/md/semester_7/theory_of_mechanism_and_machine_ii/chapter-6

## Question

Define vibration. List the harmful and useful effects of vibration. Explain the terms: period, frequency, amplitude, natural frequency, resonance, degrees of freedom, and the elements of a vibrating system.

## Short answer

Vibration is to-and-fro motion about equilibrium. Harmful effects include fatigue, noise, wear, and resonance damage; useful ones include screens, conveyors, and cleaning. Period is time per cycle, frequency is cycles per second, amplitude is max displacement, natural frequency is free vibration frequency, resonance occurs when forcing equals natural frequency, degrees of freedom are minimum independent coordinates to define motion, and a system has mass, spring, and damper.

## Answer

**Vibration** is the repeated to-and-fro motion of a body or system about its equilibrium position.

#### Effects
- **Harmful:** excess stress and fatigue failure, loosening of joints, noise, wear of bearings, discomfort to people, loss of accuracy in machine tools, and resonance damage to structures.
- **Useful:** vibrating screens and conveyors, compactors, ultrasonic cleaning and testing, musical instruments, vibratory finishing.

#### Terms
- **Period ($T$):** time for one complete cycle.
- **Frequency ($f$):** number of cycles per second, $f = 1/T$ (Hz); circular frequency $\omega = 2\pi f$.
- **Amplitude:** maximum displacement from the equilibrium position.
- **Natural frequency:** frequency at which a system vibrates freely after an initial disturbance, with no external force.
- **Resonance:** when the forcing frequency equals a natural frequency, the amplitude becomes very large (limited only by damping).
- **Degrees of freedom:** the minimum number of independent coordinates needed to define the position of all parts of the system at any time (a spring-mass has 1, a two-mass system has 2).
- **Free vibration:** system disturbed and left to vibrate. **Forced vibration:** an external force acts continuously.

#### Elements of a vibrating system
| Element | Function | Force/torque law |
|---|---|---|
| Spring (stiffness $k$) | Stores potential energy | $F = kx$ |
| Mass or inertia ($m$, $I$) | Stores kinetic energy | $F = m\ddot{x}$ |
| Damper (coefficient $c$) | Dissipates energy | $F = c\dot{x}$ (viscous) |

Springs in parallel: $k_{eq} = k_1 + k_2$. Springs in series: $\dfrac{1}{k_{eq}} = \dfrac{1}{k_1}+\dfrac{1}{k_2}$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Vibration is defined as:
   A. Repeated to-and-fro motion about an equilibrium position
   B. Continuous rotation
   C. Steady linear motion
   D. Motion in one direction only
   Answer: A. Vibration is a repeated to-and-fro motion of a body or system about its equilibrium position. (Key point: Vibration)

2. Resonance occurs when:
   A. Forcing frequency equals a natural frequency
   B. Damping is largest
   C. Amplitude is zero
   D. Frequency is zero
   Answer: A. The amplitude becomes very large, limited only by damping. (Key point: Resonance)

3. Degrees of freedom is the:
   A. Minimum number of independent coordinates needed to define the position of all parts
   B. Number of springs
   C. Number of masses always
   D. Frequency of motion
   Answer: A. A spring-mass has 1, a two-mass system has 2. (Key point: Degrees of freedom)

4. Which pairing of element and function is correct?
   A. Spring stores potential energy; damper dissipates energy; mass stores kinetic energy
   B. Spring dissipates energy; damper stores energy
   C. Mass dissipates energy
   D. Damper stores potential energy
   Answer: A. F = kx for spring, F = m x'' for mass and F = c x' for a viscous damper. (Key point: Vibrating elements)

5. For two springs in series the equivalent stiffness is given by:
   A. 1/k = 1/k1 + 1/k2
   B. k = k1 + k2
   C. k = k1 k2
   D. k = (k1 + k2)/2
   Answer: A. Series springs add flexibilities; parallel springs add stiffnesses. (Key point: Springs in series)

## Related in Theory of Mechanism and Machine II

- [Natural frequency with series-parallel springs](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Aseries-parallel-spring-mass-frequency) — Theory of Mechanism and Machine II, chapter 6
- [Undamped dynamic vibration absorber](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Adynamic-vibration-absorber-design) — Theory of Mechanism and Machine II, chapter 7
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