## The Simple Pendulum And The Concept Of Oscillation In Bodies

Suppose we have a body that is undergoing periodic motion. Then there is a relation between its displacement and time, this relation describes the path of the trajectory of the body. Now suppose inside the path or trajectory of the body undergoing periodic motion there is a point where the body is free from all external forces. The position where the body is free from all external forces is called the point or position of equilibrium. At the equilibrium position, the body is totally free from external forces and is stable and it has a tendency to remain in that position forever.

If there is some disturbance or any shift from this position of equilibrium then there will be a force or factor that will tend to bring the particle back to its original position or the equilibrium position.

Since this force has a tendency to bring back the body towards the mean position, it is trying to restore the body to its position of equilibrium position or the original state. this force acting on the body is called the *Restoring force The restoring force is opposite to the direction of displacement from the equilibrium position.*

The body under the action of the restoring force which tends to bring back the body to its original position undergoes a motion called the ** oscillatory motion or in simple words the to and from motion**.

**Mean is a statistical term**

## General Testing Of Environmental Effects

Figure 12. A simple but quantitative vibrometer for recording axial vibration of the objective relative to the slide. A cap is fitted over a low-power objective, e.g. a 10× dry, and adjusted in position until a reflective aluminum or silver film on the undersurface of a coverslip attached to the cap is in sharp focus. When the assembly is brought within a few wavelengths of a reflective coating on a slide, multiple beam fringes appear48 which can be arranged to lie approximately vertically in the image by small tilt adjustments of the slide. As shown on the right a scanned transmission image shows fringe deviations signifying height changes of more than 200 nm occurring at a few hundred Hz, due to resonances in the body of the microscope generated by ambient sound. The absolute magnitude of the height changes is known because the fringe separation is equivalent to precisely one half wavelength in air. For reflection imaging, a fully reflective mirror can be used on the slide rather than a semitransparent one. Tolansky recommends the use of silver instead of aluminum, or a rutile plate instead of a vulnerable exposed metallic coating. If the upper and lower reflecting surfaces are brought into contact the fringes become straight.

J. Spector, … K.W. West, in, 1992

## What Is Oscillatory Motion

We have studied the motion of several types.

Here we are interested in a motion that is special, in the sense that it is repetitive in nature, or in the more specific sense or in the language of physics the motion is ** periodic**.

When the repetition occurs in a particular manner or the process of repetition of the phenomenon follows a pattern then we say that the process is periodic. Ex **Halleys comet, Earths rotation. **In every such phenomenon, the event is occurring after some time period. This is the way we describe or define a periodic motion.

Suppose we are bouncing a ball aping pong ball or any other ball. In the process the person is throwing a ball with some speed towards the ground, the ball strikes the ground and rises to some height and again falls on the players hand

Let us write the equations of motion of the ball during its motion in the upward and downward direction

So for upward motion, if the initial velocity of projection was u m/s then the equation of downward motion is

At the maximum height h the ball losses all its velocity and it falls towards the ground or the players hand. So the equation for upward motion is

The equations differ in the sign of the ½ gt2 and the value of u in both cases is different.

Otherwise, the two equations are the **same** in appearance. In the discussion of the periodic or repetitive motions the words **same**, again are significant

**How this phenomenon is related to periodicity ?**

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## Overview Of Oscillations And Waves

Oscillatory motion is a type of periodic motion but in this motion, the object moves to and fro about the mean position in regular interval of time. It is important to understand that every oscillatory motion is periodic motion but every periodic motion is not oscillatory. For example, the rotation of the earth around the sun is periodic but not oscillatory. In this chapter, you will mainly have to read about Simple Harmonic Motion . SHM is the simplest form of oscillatory motion in which the restoring force is directly proportional to the displacement of the particle. Where Retarding force is a force which acts on the particle or object to bring it back to its rest position. Now let’s understand some basic terms related to Oscillatory Motion :

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Time Period – The smallest interval of time after which the motion starts to repeat itself is known as the time period. It is denoted by T.

Frequency – It represents the number of repetition of motion per unit time. In other words, it is reciprocal of the time period. It is denoted by f.

Periodic Function – A function which could be expressed by the superposition of sine and cosine functions of different time periods and suitable coefficients.

Amplitude – It is a positive constant which represents the maximum displacement of the particle in either direction. It is denoted by A.

**A wave can be classified in three manners :**

## Up And Down Oscillation

When apply a force on an object of mass attach to a spring . The spring will move a distance y above and below the equilibrium point and this movement keeps on repeating itself for a period of time . The movement up and down of spring for a period of time is called Oscillation

Any force acting on an object can be expressed in a differential equation

- F

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## What Is An Oscillation Class 7

Periodic Motion or Oscillatory Motion: When an object repeats its motion after every fixed interval of time, the motion of the object is called PERIODIC MOTION OR OSCILLATORY MOTION. The motion of pendulum starting from one extreme end to another extreme end and back to the first extreme end is called one oscillation.

## What Is Oscillations And Waves

The most basic examples of oscillation are rocking in a cradle and swinging on a swing. If you will think critically then you will realize that in both of these examples the motion is repetitive and the swing or cradle goes to and fro about a specific point. Another example is the pendulum wall clock, in which the pendulum repeats its motion periodically. If many objects come together and do oscillatory motion then they form a wave. In order to understand the former statement consider the disturbance created in a pond when you drop a stone in the still water. It will seem like the disturbance is moving outwards in the circular form. But if you will place cork on the disturbance you will see that the cork is not moving outwards it will be just oscillating where you placed it. The disturbance is a form of a wave in which the energy is transferred from one particle to another rather than actual physical transfer.

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## Oscillation Repeats Itself In A Regular Cycle

- M.S., Mathematics Education, Indiana University
- B.A., Physics, Wabash College

Oscillation refers to the repeated back and forth movement of something between two positions or states. An oscillation can be a periodic motion that repeats itself in a regular cycle, such as a sine wavea wave with perpetual motion as in the side-to-side swing of a pendulum, or the up-and-down motion of a spring with a weight. An oscillating movement occurs around an equilibrium point or mean value. It is also known as periodic motion.

A single oscillation is a complete movement, whether up and down or side to side, over a period of time.

## Q1 Give Two Applications In Which Resonance Plays An Important Role

**Answer****:**

**1. Radio and Resonance:** Tuning a radio is the best example of electrical resonance. When we have to listen to a specific station, we turn the knob at different points. By turning the knob, we change the natural frequency of the electric circuit of the receiver. We do this in order to make the natural frequency equal to the transmission frequency of the radio station. And when the two frequencies match then the energy absorption will be maximum so in that way we only listen to a specific radio.

**2. Magnetic Resonance Image :** Another example of resonance is magnetic resonance scanning. It has greatly enhanced medical diagnoses. In this technique, strong radiofrequency radiations are used to cause nuclei of atoms to oscillate. At the point when resonance occurs, the energy is absorbed by the molecules. This pattern of energy absorption is then used to produce a computer-enhanced photograph that gives us detail information about the scanned area.\

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## Period And Frequency In Oscillations

In the absence of friction, the time to complete one oscillation remains constant and is called the period . Its units are usually seconds, but may be any convenient unit of time. The word âperiodâ refers to the time for some event whether repetitive or not, but in this chapter, we shall deal primarily in periodic motion, which is by definition repetitive.

A concept closely related to period is the frequency of an event. **Frequency** is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is

## Q7 Explain What Is Mean By Damped Oscillations

**Answer:**Oscillations are said to be damped if they are changed by some opposing forces. Ideally the total energy of oscillation remains constant. It is conserved in all oscillations like in mass attached to a spring, body moving in circular motion and also in case of simple pendulum, according to which if we disturb an oscillating body from its equilibrium, it will remain in oscillation until we stop it, but in real it is not so. All oscillating objects stop oscillation after some time due to frictional forces. So, oscillation does die out with the time until energy is continuously supplied to the body. For example, in case of swing, to keep the swing in continuous oscillation we must push it continuously in a specific direction and at a specific time. So we can say that

**The oscillation in which the amplitude of oscillation become smaller and smaller with the time is called damped oscillation.**

The damping of oscillation is also very useful phenomena, the concept of damping is used in the shock absorbers i.e. in the suspension system of our cars and motorcycle etc. which provide us with a comfortable ride even on rough and bumpy surfaces.

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## Definition Of An Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging back and forth, or a spring compressing and stretching, the basic principle of oscillation maintains that an oscillating particle returns to its initial state after a certain period of time. This kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a particle in the system. In every oscillating system there is an equilibrium point at which no net force acts on the particle. A pendulum, for example, has its equilibrium position when it is hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this point, however, the pendulum will experience a gravitational force that causes it to return to the equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will experience a force returning it to the equilibrium point. If we denote our equilibrium point as *x* = 0, we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the particle from the equilibrium point.

## Q8 What Is The Total Distance Covered By A Simple Harmonic Oscillator In A Time Equal To Its Period The Amplitude Of Oscillation Is A

**Answer:**The time period is defined as the time required to complete one vibration. Thus in one vibration, the oscillator moves from one extreme position say B towards a mean position say O, continues its moved to the other extreme position say C and then returns back to the first extreme position B after passing through the mean position O. The distance from mean position to extreme position i.e. amplitude OB = OC = A so the total distance covered in one vibration is BO+ OC+ CO+ OB= A + A + A + A = 4A

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## Example : Determine The Frequency Of Two Oscillations: Medical Ultrasound And The Period Middle C

We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Lets try one example of each. A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs. What is the frequency of this oscillation? The frequency of middle C on a typical musical instrument is 264 Hz. What is the time for one complete oscillation?

**Strategy**

Both questions and can be answered using the relationship between period and frequency. In question , the period\boldsymbolis given and we are asked to find frequency\boldsymbol.In question , the frequency\boldsymbolis given and we are asked to find the period\boldsymbol.

**Solution a**

Solve to find

\boldsymbol}.

**Discussion a**

The frequency of sound found in is much higher than the highest frequency that humans can hear and, therefore, is called ultrasound. Appropriate oscillations at this frequency generate ultrasound used for noninvasive medical diagnoses, such as observations of a fetus in the womb.

**Solution b**

The time for one complete oscillation is the period\boldsymbol:

\boldsymbol\boldsymbol}.

**Discussion **

## What Is Oscillation And Vibration

Oscillation vs Vibration

Oscillation is a definite distance covered by the movement about its equilibrium position, vibration is referred to the physical change brought about due to movement of the body. Oscillation can be seen in the swinging of a pendulum clock and vibration in the plucking of guitar string.

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## Basic Concepts Of Oscillations And Waves

- Complete back-and-forth movement of the oscillating body is called a
**period**. - The
**amplitude**is the extent of a wave measured from the highest peak down to the zero position. - The
**period duration T**is the time needed for an oscillating body to move back and forth, i.e. to fulfill one period. It is often referred to as the**period**. **Frequency**is the quotient of the number of periods and the time required for it.**Elongation**is defined as the current distance from the zero position.**Circular frequency**is the angular velocity of a circular movement whose projection on a straight line results in a harmonic oscillation.- The
**phase**is specified by the two oscillation parameterselongation and timeand is indicative of the current state of oscillation. - The
**damped oscillation**is an oscillation in which the amplitude of the oscillating quantity decreases with time because of frictional forces. **Undamped oscillations**have constant amplitudes. It is necessary for the energy supplied to the vibrating system to be maintained. In the case of constant small energy losses, a sustained undamped oscillation, in reality, is only approximately possible. In order to create a real undamped oscillation, the energy losses that occur must be compensated for by a regular energy supply.

## Now We Need To See What Is The Cause Of The To And Fro Motionhow Does This To And Fro Motion Generate

**Now we need to see what is the cause of the to and fro motion?**

**How does this too and fro motion generate?**

**If we have a body that was in equilibrium and it was disturbed or moved away from its mean or equilibrium position then the restoring force acts on the body to bring it back to its original position**

**So the equation of motion is something like**

**Ma=-sx**

**where M is the mass of the body, a is the acceleration, K is the stiffness constant and x is the amount of displacement from the equilibrium position**

** the equation above reduces to a differential equation.**

**We can write the above equation in a different form**

**And this from is special**

** the ratio of the spring or stiffness constant and the mass of the body has a special significance. Both are kinds of inertia. To understand what this ratio is let us do the dimensional analysis.**

**This T is defined as the Time period of oscillation. The time to complete one oscillation is defined by the ratio of the two inertia factors**

So what we define in oscillation is that the body moves towards each **extreme position** from the mean position and then returns back to the mean position.

**A and C are extreme positions .**

**Why they are called extreme positions?**

At positions A and C, there is a complete conversion of KE to PE

The PE at A or C is completely changed into KE at position B

*So oscillation can now be defined as the periodic change in the form of energy from KE to PE and then back from PE to KE*

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