Oscillatory motion

Periodic or oscillatory motion is defined as a motion that repeats itself. An object in such motion vibrates around an equilibrium position due to a regulating force or torque. Many phenomena, including electromagnetic waves, alternating current circuits, and molecules, require this motion to be studied. For a vibration to occur, two factors must be fulfilled: stiffness and inertia. An object in such motion vibrates around an equilibrium position due to a regulating force or torque. Such force or torque attempts to restore (return) the system to its equilibrium position, irrespective of whatever direction it is moved.

Oscillatory motion

The pendulum’s motion is an example of oscillatory motion. When ideal conditions exist, any object’s oscillatory motion will never come to an end because there is no friction due to air under the ideal state.

Oscillatory motion is a type of motion in which an object moves over a spot repeatedly. Because there will be no air to stop the item in oscillatory motion friction, the ideal situation can be achieved in a total vacuum.

The vibration of strings and the movement of a spring are both oscillatory motions in the mechanical world and are the same as mechanical vibration. Periodic motion must not be confused with oscillatory motion. Objects in periodic motions replicate their motion after a set amount of time, whereas objects in oscillatory motions replicate their motion over a defined position.

Types of Oscillatory Motion

Linear Oscillatory Motion and Circular Oscillatory Motion are the two main types of oscillatory motions.

In linear motion, the item moves left and right or up and down.

 The following are some examples of linear motion:

The sound of musical instruments’ strings vibrating,

Floating of ships or large boats on the water and fluid movement in a U-tube column.

When the object moves left to right in circular motion, it does so in a circular way. The following are some examples of this type of motion:

In a half hollow sphere, the motion of a solid sphere

The pendulum in a watch moves back and forth.

A strung object is hung from a nail.

A wheel’s rotation.

The oscillatory motion’s equilibrium position is the place at which oscillations exist, and the oscillating object must pass through this point during each oscillation. The oscillating object comes to a stop on this point after some time when the oscillatory motion quits due to friction in the medium in which it is oscillating.

Oscillatory motion is not the same as periodic motion. Every oscillatory motion is inherently a periodic motion, although not every periodic motion is oscillatory. Oscillatory or non-oscillatory periodic motions exist.

Oscillatory motion equation

Simple Harmonic Motion is a simple type of oscillatory motion (SHM). The restoring force in this motion is normal to the displacement from the equilibrium position. This is termed as Hooke’s law.

The following example will help you understand Hooke’s law. Assume a mass m block is tied at one end with a long spring (spring constant k) and the other end is anchored to the wall. The spring tries to return the block to its original place when it slides horizontally away from the wall. resulting in oscillatory motion. Hooke’s law expresses the restoration force that attempts to restore the deformation of a spring.

Fs = -kx, here the negative sign represents that the force is against the displacement.

The restoring force will strive to return the block to its equilibrium position when it is shifted to x=A and released. However, when black reaches its equilibrium position (x=0), The block’s potential energy is transformed to kinetic energy, causing it to cross the equilibrium point to the other side ,till x=-A. Block advances to the right again at this point, taking the position x=A. The motion will continue in this manner until the friction force acts to stop the block. The restoring force is equivalent to the frictional force. As a result of Newton’s second law, frictional force is given as:

 Fr=ma here m = mass of the block and a = acceleration of the block.

 Fs= Fr 

Or

 ma= -kx

It can be written in terms of x 

 m d²x ⁄dt²= -kx 

Or 

m d²x ⁄dt²+kx=0 

Or 

 d²x⁄dt²+kx =0

Here ω=√k/m that gives angular frequency of the system.

Uses of oscillatory motion

At both sides of its rest position, the spring’s motion is routinely repeated in equal durations of time. When the oscillatory body (spring) passes its rest position, its velocity is quite high. When the oscillating body (spring) moves away from its rest position, its velocity falls until it approaches zero at the maximum displacement.

Oscillatory motion can be seen in the following examples:

Pendulum, Spring, Tuning fork Swing motion and stretched string (Example: Guitar).

The motion of atoms in molecules and the movement of the Earth’s crust during earthquakes.

The rotary bee’s motion is classified as a periodic motion since it is repeated at regular intervals, but it is not an oscillatory motion because it is not repeated at regular intervals.

Conclusion

Periodic or oscillatory motion is defined as a motion that repeats itself. The pendulum’s motion is an example of oscillatory motion. The oscillatory motion’s equilibrium position is the place at which oscillations exist, and the oscillating object must pass through this point during each oscillation. Simple Harmonic Motion is a simple type of oscillatory motion (SHM). The restoring force in this motion is normal to the displacement from the equilibrium position. This is known as Hooke’s Law. Linear Oscillatory Motion and Circular Oscillatory Motion are the two main types of oscillatory motions.