Need Help?

Get in touch with us

The component learnSearchBar has not been created yet.

bannerAd

Terms Related to Oscillations

Aug 23, 2022
link

Key Concepts

  • Terms Related to Oscillatory Motion
  • Oscillatory Motion of a Pendulum
  • Oscillatory motion of a spring and Mass System

Introduction:

The motion of a mass attached to a string and a pendulum are also examples of periodic motion but of different types. All these objects execute to and fro, or back and forth motion periodically about a mean position such a motion is termed an oscillatory motion. 

We describe an oscillatory motion using some variables such as: 

  • Time Period 
  • Frequency 
  • Displacement 
  • Amplitude 

Explanation:

Oscillations of a Simple Pendulum: 

The oscillation of a simple pendulum can be demonstrated by the swing of a pendulum. A simple pendulum consists of a massive object called the bob, suspended by an unstretched string of length L. After the bob is pulled to one side and released, it swings back and forth as shown in the figure. 

Oscillations of a Simple Pendulum
  • A pendulum bob executes an oscillator motion about an equilibrium position. 
  • The starting position of the pendulum is called the mean position or equilibrium position labeled as A. 
  • The bob moves to and fro about its mean position labeled as A and rises to extreme positions on both sides labeled as C and B and repeats its motion. 

For one complete oscillation, the bob can follow anyone the following paths: 

One complete oscillation by a simple pendulum

Time period: 

The smallest interval of time after which the motion is repeated is called its time period.  

parallel

The time taken to complete one oscillation is known as the time period. 

The time period is denoted by the letter T. 

The S.I. unit of time period is second (s). 

Frequency: 

The reciprocal of the time period or the number of oscillations a pendulum performs in one second is called the frequency of the periodic motion.  

It is represented by the symbol “ν ” or “f “. 

parallel

The relation between ν and T is: 

ν = 1/ T 

The S.I. unit of ν is thus (1/sec) or hertz (Hz). 

Displacement: 

The motion of a simple pendulum can be described in terms of the angle “θ” it makes with the vertical as a function of time. 

It is convenient to measure the angular displacement of the bob from its equilibrium position. 

Angular displacement of the simple pendulum from the equilibrium position

Amplitude: 

The maximum angular displacement of the bob from its equilibrium position, i.e., when it moves from A→B or A→C is called its amplitude. 

The S.I. unit of amplitude is radian or meter. 

Oscillations of Spring and Mass System: 

Oscillations of a spring and a mass system

Horizontal Oscillatory motion of a Spring and a Mass System: 

The horizontal oscillatory motion of a spring and a block system is one of the simplest types of back-and-forth periodic motion. Let us assume that a mass moves on a frictionless horizontal surface. When the spring is stretched or compressed and then released, it oscillates back and forth about its unstretched position. 

Horizontal Oscillatory motion of a spring and a mass System

Observations: 

  • The direction of the elastic force acting on the mass is always opposite to the direction of the block’s displacement from equilibrium (x = 0). 
  • When the spring is stretched to the right, the spring force pulls the mass to the left. 
  • When the spring is unstretched, the spring force is zero.  
  • When the spring is compressed to the left the spring force is directed to the right. 

Conclusion: 

The amplitude of the mass-spring system is the maximum displacement amount the spring is stretched or compressed from its equilibrium position. 

Amplitude = maximum displacement from the equilibrium = X 

Time period = Time it takes to move from 0 →(+X) → 0 → (-X)→ 0  

Frequency = Number of oscillations it makes in one second. 

Frequency = 1/Time period 

Vertical oscillatory motion of a spring and a block system: 

Observation: 

The direction of the elastic force acting on the mass is always opposite to the direction of the block’s displacement from equilibrium (Y = 0). 

Vertical oscillations of a spring and a mass System-1

Observation: 

When the spring is stretched down (Y = -Y), the spring force pulls the mass up. 

When the spring is unstretched (Y = 0), the spring force is zero.  

When the spring is compressed up (Y = +Y), the spring force pulls the mass down. 

Conclusion: 

The amplitude of the mass-spring system is the maximum displacement amount the spring is stretched or compressed from its equilibrium position. 

Vertical oscillations of a spring and a mass System-2

Amplitude = maximum displacement from the equilibrium = X 

Time period = Time it takes to move from 0 →(+X) → 0 → (-X) → 0  

Frequency = Number of oscillations it makes in one second. 

Frequency = 1/Time period 

Question: 

A simple pendulum takes 52 seconds to complete 20 oscillations. What is the time period of the pendulum? 

Answer:  

We know that time period is the time required to complete one oscillation: 

Time period = Total Time taken for oscillations / No. of oscillations  

Time period = 52 / 20 = 2.6 Second 

The time period of the pendulum is 2.6 seconds 

Summary

  • We describe oscillatory motion using some variables such as: Time Period, Frequency, Displacement Amplitude
  • Time period: The smallest interval of time after which the motion is repeated is called its time period.
  • Frequency: The reciprocal of the time period or the number of oscillations a system performs in one second is called the frequency of the periodic motion. S.I. unit of frequency is Hertz.
  • Amplitude: The maximum angular displacement or displacement of a body from its equilibrium position is called amplitude. The S.I. unit of amplitude is radian or meter.

Comments:

Related topics

Define Position Time Graph and its Types

Key Concepts • Slope of a graph • Position time graph • Slope of s-t graph = Velocity • Types of position time graphs Introduction An object in a uniform motion covers equal distances in equal intervals of time. This also indicates that it moves at a constant velocity. When its position at different instants […]

Read More >>

Magnetic Field Lines: Definition, Explanation and Q&A

Key Concepts Magnetic Field Magnetic Field Lines properties of magnetic field lines Uniform and non uniform magnetic lines Introduction Two magnets when placed close to each other attract and stick to each other. However, if we go on increasing the distance between them, the attraction between them reduces gradually to such an extent that they […]

Read More >>

The Life Cycles of Stars: Meaning and Example

Key Concepts Stars Analysis of starlight Composition of stars Stars’ temperature Size and mass of stars Stages of life cycle of a star Introduction Stars are huge, shining balls of extremely hot gas (known as plasma) in space. The Sun is our nearest star. During the nighttime, many other stars are visible to the naked […]

Read More >>

Mirror Formula

Key Concepts New cartesian sign convention Mirror formula Solving problems using the mirror formula Introduction When dealing with the reflection of light by spherical mirrors mathematically, a set of sign conventions is followed, called the New Cartesian Sign Convention. According to this convention, the pole of a spherical mirror is taken as the origin and […]

Read More >>

Other topics