Vibration is defined as:

Repeated to-and-fro motion about an equilibrium position

Degrees of freedom is the:

Minimum number of independent coordinates needed to define the position of all parts

Which pairing of element and function is correct?

Spring stores potential energy; damper dissipates energy; mass stores kinetic energy

Spring dissipates energy; damper stores energy

Practice · 5 marks

Vibration terms, effects and elements

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.

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.

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: $\dfrac{1}{k_{eq}} = \dfrac{1}{k_1}+\dfrac{1}{k_2}$ .

✓ Answer checked by Claude Opus 5.5 (high effort)

Natural frequency with series-parallel springs · Theory of Mechanism and Machine II, chapter 6
Undamped dynamic vibration absorber · Theory of Mechanism and Machine II, chapter 7
Natural frequency by energy method · Theory of Mechanism and Machine II, chapter 6
Forced damped two-degree-of-freedom system · Theory of Mechanism and Machine II, chapter 7
Lateral vibration of a simply supported beam · Theory of Mechanism and Machine II, chapter 10
Two-rotor torsional system frequency · Theory of Mechanism and Machine II, chapter 6
Forced vibration amplitude and resonance · Engineering Physics, chapter 1 · asked 2×
Degrees of freedom and generalised coordinates · Engineering Mechanics, chapter 9
CFCs in ozone depletion and harmful effects · Engineering Chemistry, chapter 3
Water pollutants, harmful effects, control measures · Engineering Chemistry, chapter 3

All Theory of Mechanism and Machine II chapter 6 questions →

Vibration terms, effects and elements

Effects

Terms

Elements of a vibrating system

Related questions