# Unit of Vibration

## What is Vibration in Physics?

The word vibration is derived from the Latin word “vibrationem” which means "shaking or brandishing".

Vibration is the back and forth periodic motion of an elastic material. Such an oscillation is a mechanical phenomenon that occurs in an equilibrium position.

In many places, you may find the real-life applications of vibration, such as the motion of a pendulum, the motion of a tuning fork, etc.

In this article, you will learn vibration definition Physics, the SI unit of vibration, and vibration measurement units in detail.

### Vibration Definition Physics

Vibration means the act of vibrating or the condition/instance of being vibrated. In Physics, vibration has the following properties:

• It is a rapid linear motion of a particle or an elastic medium about an equilibrium position.

• A single cycle of vibrating motion.

• A periodic motion/process about an equilibrium position, such as the periodic displacement of air and the propagation of sound from the microphone.

### Sound and Vibration

The properties of sound and vibration are nearly similar. Sound is the pressure waves that are generated by vibrating structures such as vocal cords; these pressure waves can also induce the vibration of structures, such as an eardrum. Hence, attempts to reduce noise are mostly related to the issues of vibration.

The vibration symbol during connectivity is:

### Damping Free Vibration

To proceed with the investigation for the mass-spring-damper, consider the damping is negligible and no external force is applied to the mass that means it is a free vibration.

Now, the force applied to the mass by the spring is proportional to the amount with which the spring is stretched by "x" (presuming that the spring is already compressed because of the weight of the mass).

The proportionality constant, k, is the hardness of the spring and has units of force/distance, a.k.a lbf/in or N/m. The negative sign indicates that the force always opposes the motion of the mass attached to it, so the equation for this statement is given by:

F = - kx

According to Newton’s second law of motion, the force generated by the mass is proportional to the acceleration of the mass as provided in the following equation:

$\sum F$ = ma = mx = m$\frac{\mathrm{d}^{2}x}{\mathrm{d}t^{2}}$

The sum of the forces on the mass generates an ordinary differential equation as;

ma + kx = 0

For a simple mass-spring system, the undamped natural frequency fn is given by:

fn = $\frac{1}{2}$π $\sqrt{\frac{k}{m}}$

## Types of Vibration

### 1. Free Vibration

It occurs when a mechanical device is set in motion with a starting input and allowed to vibrate./oscillate freely.

Examples of this type of vibration are:

1. Pulling a child back on a swing and letting it to-and-fro.

2. Hitting a tuning fork and letting it oscillate.

3. The mechanical device vibrates at high natural frequencies and damps to motionlessness.

2. Forced Vibration

When time-varying distortions like load, displacement or velocity are applied to a mechanical system, the disturbance can be periodic, a steady-state input, a transient input, or a random input.

The periodic input can either be a harmonic or a non-harmonic disturbance.

Examples of these types of vibrations involve:

1. A washing machine shaking because of an imbalance.

2. Vibration caused in vehicles by an engine or uneven road.

3. The vibration of a building during an earthquake.

Point To Note:

For linear systems, the frequency of the slow vibrations results from the application of a periodic, harmonic input and is equal to the frequency of the applied force or motion. The response magnitude is always dependent on the actual mechanical system.

### 3. Damped Vibration

When the energy of a vibrating system gradually dissipates by friction or other resistances, the vibrations are considered damped. The vibrations reduce gradually or may vary in frequency or intensity or reduce and the system rests in its equilibrium position.

A well-known example of damped vibration is the vehicular suspension dampened/lessened by the shock absorber.

### SI Unit of Vibration

The SI unit of vibration or the vibration unit is Watts per meter square.

### Vibration Measurement Units

Talking about the vibration measurement units or the vibration amplitude measurement, vibration is generally expressed by the units of Frequency, Velocity, Acceleration, and Displacement which are denoted by English alphabets, F, V, A, and D.

If we look at it practically, vibration is most often an intricate summation of various frequencies at different amplitudes.

### Do You Know?

Vibration can be desirable for the motion of a tuning fork, the reed in a woodwind instrument/harmonica, a mobile phone, or the knob of a loudspeaker.

However, in many cases, vibration is undesirable because it wastes energy and creates unwanted sound.

For example, the vibrational motions of mechanical devices like heavy-duty vehicle engines, electric motors, or any device in function are unwanted. Such vibrations may be caused by the imbalance or irregularity in the rotating parts of machines, uneven friction, or the meshing of gear teeth (contact with adjacent gearwheel).

Careful designing of these devices can minimize unwanted vibrations.

Q1: Describe an Oscillatory System.

Ans: One of the simplest and finest mechanical oscillating systems is a weight attached to a linear spring offered to the weight and tension. A system may be placed on an air table or ice surface. The system is said to be in an equilibrium state when the spring is static. However, when the system is displaced from the equilibrium, there is a net restoring force on the mass, which tries to bring it back to its equilibrium position.

However, in moving the mass back to the equilibrium position, it acquires a momentum that keeps it moving beyond that position, and therefore, establishing a new restoring force on the opposite side.

If a constant force, viz: gravity gets added to the system, the position of equilibrium shifts. The time taken for an oscillation to occur is often conferred the oscillatory period.

Q2: What is the Importance of Studying Mechanical Vibrations?

Ans:

1. Faults in design & manufacturing cause excessive and unpleasant stresses in the rotating system because of vibration, which leads to failure.

2. Vibration causes rapid wear and tear of the machine parts such as bearing and gears.

3. Vibration Causes a loosening of parts from the machines which may lead to accidents.

4. Excessive deformation of the wheel of the Locomotive can leave the track due to excessive Vibration that results in Accident or heavy loss.

5. Building structures bridges fail because of the vibration caused by moving vehicles.

6. Excessive vibration is dangerous for humans.

7. The Study of Vibration is Essential for a Design Engineer to minimize the vibration effects on Mechanical Components by designing them carefully.

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