# Oscillatory motion, definition with examples for better understanding.

We are very much familiar with oscillatory motion in one or more ways. Swinging a swing in the park by children is a bright example of oscillatory motion. In fact, the to-and-fro motion of an object from its mean position is referred to as oscillatory motion.

## Oscillatory motion, definition

We are very much familiar with oscillatory motion in one or more ways in our day-to-day life. Swinging a swing in the park by children is a bright example of oscillatory motion. In fact, the to-and-fro motion of an object from its mean position is referred to as oscillatory motion. The ideal condition for such a system is that the object can be in oscillation forever in absence of friction, however, in the real world, such happening is not possible as the object has to settle into equilibrium somehow.

The equilibrium position of the oscillatory motion is one about which the oscillation occurs and during oscillation, the object has to pass through the point without any deviation. After some time the oscillation of the object stops at the equilibrium position due to the friction of the medium.

Let us see the image below, for a better understanding. In the mage the object is suspended from a point, O and, it has the equilibrium point at B. The object oscillates from point A to point C about point B.

In mechanical oscillation, the term vibration is used for oscillation when the object moves at high frequencies, otherwise when it moves slowly it is called oscillation.

## Types of oscillatory motion

The oscillatory motion may be of two types

• Linear oscillation
• Circular oscillation

### Linear oscillation;

In linear oscillation, the object moves left and right, up and down about a fixed point of equilibrium.

#### Examples

• The vibration of strings of musical instruments- Musical instruments like guitars, violin, etc. contains vibrating strings. When the strings of the musical system strike, it vibrates back and forth, causing sound waves in linear oscillation.
•   Movement of spring in mass-spring system-Such a system consists of a spring attached to a mass at one end and the other end is kept free. When the spring is stretched or compressed it exerts a force to restore its original shape, causing it to oscillate forth and back around its equilibrium points.
• Flopping of wings of birds and butterflies-Flying birds and butterflies are very enjoyable to watch. The flipping wings (of the above creatures)are around a fixed point of equilibrium, where the wings back and forth while flying.
• Floating of ships in the sea– In the sea or ocean ships and big containers float with up and down motion along a fixed point of oscillation.
• Sound waves-We are aware of the fact that sound waves are longitudinal waves that travel through a medium like air or water. When a sound wave is generated it oscillates forth and back around a fixed point of oscillation, which is linear in nature.

### Circular oscillation;

In circular oscillation, objects move in a circular path around a fixed point and oscillate back and forth along that path.

#### Examples-

1. A freely hanging bob– A freely hanging bob of a simple pendulum swings in a circular path about a fixed point of oscillation forward and backward.
2. A swing– In a park, we have seen the sight of swinging by kits. A swing moves in a circular path about a fixed point of oscillation back and forth, many times.
3. A spinning top-A toy like spinning top is another example of circular oscillation. When it spins it rotates around its axis back and forth, causing circular oscillation.
4. Pendulum– The pendulum moves back and forth about a fixed point of oscillation in a circular way.
5. A Ferris wheel-. Riding a Ferris wheel is amazing. When one rides it, that moves in a circular path around a fixed point of oscillation, as the wheel rotates, justifying circular oscillation.

### Classification of oscillatory motion

The oscillatory motion may be further classified into the following categories;

#### Simple harmonic motion-

Simple harmonic motion is a special type of periodic motion which is also referred to as a type of oscillatory motion, where an object moves forth and back about its equilibrium position in a systematic pattern. In such a motion, the restoring force is directly proportional to its displacement from its equilibrium position. This phenomenon is known as Hooke’s law, which can be explained by the following Example-

Let us take a block of mass m tied up with a long spring, (with spring constant k,)at one end and another end is fixed on one point of the wall, When the block moves away from the wall horizontally, the spring tries to restore its original shape and due to this oscillatory motion begins. The restoring force can be expressed by Hooke’s law-

F=-kx

where,

• F is the restoring elastic force exerted by spring (N)
• k is the spring constant(Nm-1)
• x is the displacement from the equilibrium position.

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#### Damped oscillation-

Damped oscillation is a type of oscillation where the amplitude of the oscillation decreases over time due to friction or any other dissipative forces. It may be natural or manmade/artificial. Example-A weight on a spring.

#### Forced oscillations-

When an object oscillates in rhythm by the influence of an external force is called forced oscillation. Example-A child on a swing pushed by an adult.

#### Coupled oscillation-

When two or more objects are interconnected and their oscillatory motion is interdependent on each other, is referred to as coupled oscillation motion. Example-Motion in a system where two pendulums are connected by a spring.

#### Nonlinear oscillation-

In such types of oscillation, the motion behaves rather in a complex way than in a simple sinusoidal pattern. Example- Motion of a metronome on a moving platform.

### Oscillatory motion is not to be confused with periodic motion

One must not be confused between periodic motion and oscillatory motion. Objects in periodic motion repeat their motion after a fixed duration of time, however, in oscillatory motion, the objects repeat their movement about a fixed point of oscillation. Each oscillatory motion is periodic motion but each periodic motion may or may not be oscillatory in nature

## Applications of oscillatory motion

Oscillatory motion has many applications in science and technology, as well as in daily life.

• Timekeeping– Time and tide wait for none. Timekeeping is very important for human existence and its development on earth. The oscillatory motion of a pendulum or quartz crystal is used in clocks and watches for indication of actual time.
• Motion control– Motion control is another important application of oscillatory motion found in the suspension system of a car to regulate the movement of the vehicle. Its application is also found in the motion control of a robotic arm.
• Electrical circuit-Use of oscillatory motion is made in electrical circuits to create and manipulate electrical signals in devices like radio transmitters, antennas, etc.
• Sound and vibration-In acoustics sound and vibrations play very important roles and are examples of oscillatory motions.
• Material testing-For the testing of the properties of materials, oscillatory motion is used. The vibrating probe technology is used to measure the stiffness of biological tissues or the use of an oscillating beam to measure the elastic module of materials.
• Medical imaging– The application of oscillatory motion in medical applications is a significant development in the health sector. In the applications like ultrasound, high-frequency sound waves are used to create images of internal organs for better diagnosis and treatment.

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## Conclusion

We are very much familiar with oscillatory motion in one or more ways. Swinging a swing in the park by kits is a bright example of oscillatory motion. It may be of different types and its applications are found in science and technology, medical imaging, and other ways

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