# Chapter 14 – Oscillations

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

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Read on to know more about the topic of Oscillations and understand its basic concepts, its definition, and other vital subheadings that would help you learn and revise the concepts.

What are Oscillations?

Oscillations are variations in time, of a fixed measure, observed in the swinging motion of a pendulum. What we generally refer to as vibrations are a type of oscillations known as mechanical oscillations. The only notable difference between oscillations and vibrations is that the frequency of the former is greater than that of the latter.

Oscillations occur naturally in physical systems of the world as well as in human bodies and other biological systems. To properly understand oscillations, it is essential to have sound knowledge of its underlying fundamentals and related concepts. Below are some significant sub-topics of Oscillations that will enable you to attain a firm grasp over the subject.

#### Periodic And Oscillatory Motions

Thus, a motion that repeats itself at regular intervals of time is called periodic motion. Any physical body that undergoes a periodic oscillatory motion contains an equilibrium position in its path. This position is the point at which no external force acts on the body, and if and when the body comes at rest at the equilibrium position, it is likely to remain at rest until it is displaced from the position. This displacement of a body from its position of equilibrium, in turn, creates oscillations or vibrations.

Therefore, it can be deduced that every oscillatory motion is periodic. However, the reverse of this deduction does not hold true, and it is not necessary that every periodic motion would be oscillatory in nature. This difference is crucial for understanding periodic and oscillatory motions. For example, most circular motions are periodic but not oscillatory in nature.

The following formulae can be used to calculate the height at which the motion takes place are:

h= ut+ ½ gt2 for downward motion, and

h= ut- ½ gt2 for upward motion, where g is gravity constant, and t is the time of the motion.

#### Simple Harmonic Motion

The simplest form of oscillatory motion is called  Simple Harmonic Motion (SHM). SHM is not periodic in nature and is a function of time as it the motion of a body oscillating back and forth on an axis between two fixed points. The body’s displacement from its mean position is directly proportional to the force acting on it, and this force is always directed towards the mean position.

The formula for representing SMH is:

x (t) = A cos (ω t + φ) (14.4)

Where A, ω and φ are constants and is x is the displacement of the body.

Some concepts to pay attention to while studying SMH are:

#### Simple Harmonic Motion And Uniform Circular Motion

Uniform Circular Motion is a projection of a Simple Harmonic Motion, where the position x of a body inside a circle’s radius is calculated by:

x(t) = A cos (ωt + φ )

#### Velocity And Acceleration in Simple Harmonic Motion

The velocity of a body in Simple Harmonic Motion is calculated by the following,

v = ω A

where ω is the time of angular speed, and A is the radius of the circle the body is inside during motion.

The acceleration of the velocity is calculated by:

v(t) = –ωA sin (ωt + φ )

Where t is the tangent of the circle at the point where the body in motion is located at any given instant.

#### Force Law For Simple Harmonic Motion

Newton’s second law of motion is applied to calculate the force law for Simple Harmonic Motion, the formula for which is:

F (t) = ma

Where m is the mass of the body in motion.

#### Energy In Simple Harmonic Motion

The energy in Simple Harmonic Motion is calculated using Hooke’s law, the formula for the calculation being:

F = −kx

Where F is force, x is the displacement of the body from equilibrium, and the key is the force constant.

#### Some Systems Executing (SHM) Simple Harmonic Motion

While there are no examples of a body exhibiting pure SHM, both the Spring and a Simple Pendulum are some systems executing Simple Harmonic Motion, former being the simplest example of the same.

#### Damped Simple Harmonic Motion

Damped Simple Harmonic Motion occurs when a non-conservative force dissolves the energy of the body in motion, causing it to return to its position of equilibrium as fast as possible.

#### Forced Oscillations And Resonance

Forced oscillations occur when an external displacement acts on a body to make it oscillate, and resonance happens when a body oscillates at its natural frequency.

#### FAQs

Q1. What is an oscillation in physics?

A. In the simplest terms, oscillation is repetition in a body in motion.

Q2. What does oscillation mean?

A. Oscillation means the to and fro movement of a body in motion at a given frequency. What we generally refer to as vibrations are a type of oscillations.

Q3. What is the formula for oscillation?

A. Different types of oscillations are calculated using different formulas, like h= ut+ ½ gt2 for downward motion and for SMH it is x (t) = A cos (ω t + φ) (14.4), etc.

Q4. What are the types of oscillation?

A. There are two types of oscillation: damped and undamped.

We hope that this write-up helped you understand the key concepts of Oscillation. To gain more clarity and knowledge of these concepts, you can avail our video library on the MSVgo app. The videos have been made by our physics experts and explain each topic in great detail, making sure they meet your requirements. You can also check our video library on our app to find everything you need to ace your next physics examination.

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