Skip to main content

SIMPLE HARMONIC MOTION

By

 SIMPLE HARMONIC MOTION

A body is said to be vibrating if it moves back and forth or to and fro about a point. Another term for vibration is oscillation. A special kind of vibratory or oscillatory motion is called the simple harmonic motion

A spider detects its prey due to vibration produced in the web.

MOTION OF MASS ATTACHED TO A SPRING

One of the simplest types of oscillatory motion is that of horizontal mass-spring system . If the spring is stretched or compressed through a small displacement x from its mean position, it exerts a force F on the mass. According to Hooke’s law this force is directly proportional to the change in length x of the spring.





                                                     F = - k x

where x is the displacement of the mass from its mean position O, and k is a constant called the spring constant defined as

                                                    k = - F

 The value of k is a measure of the stiffness of the spring. Stiff springs have large value of k and soft springs have small value of k.

                                                   F = ma

                                                  k  = - ma/x

                                                 a = - x k/m

                                                  a ✔-x

It means that the acceleration of a mass attached to a spring is directly proportional to its displacement from the mean position. Hence, the horizontal motion of a mass-spring system is an example of simple harmonic motion

The negative sign  means that the force exerted by the spring is always directed opposite to the displacement of the mass. Because the spring force always acts towards the mean position, it is sometimes called a restoring force. 

A restoring force always pushes or pulls the object performing oscillatory motion towards the mean position. 






This process is repeated, and the mass continues to oscillate back and forth about the mean position O. Such motion of a mass attached to a spring on a horizontal frictionless surface is known as Simple Harmonic Motion (SHM). The time period T of the simple harmonic motion of a mass ‘m’ attached to a spring is given by the following equation:


                                            T =2π✔m/k

Location: Pakistan

Comments

Post a Comment

Popular posts from this blog

THERMAL PROPERTIES

By
THERMAL PROPERTIES OF METER  The crocus flower is a natural thermometer. It opens when the temperature is precisely 23 degree centigrade and closes when the temperature drops. Liquid in Glass Thermometer Construction: A liquid in glass thermometer has a bulb whit a log capillary tube of uniform and fine bore. PRINCIPLE      Liquid in glass thermometer is made on he principle of expansion of heating.       A suitable liquid is filed in the bulb. When  we touch the bulb with a hot body, the liquid in it expands and rises in the tube. the glass stem of a thermometer is thick and acts as a cylindrical lens. This makes it easy to see the liquid lever in the glass tube. THE MERCURY IN GLASS THERMOMETERS\ Mercury freezes at -39 degree centigrade and boils at 357 degree centigrade. Mercury has all the thermometer properties. So mercury is one of the most suitable thermometer materials. Murcury in glass thermometer are widely used in laboratories, clinic and house to measure tempertatures in th
Post a Comment
Read more

TIME SERIES ANALYSIS

By
Introduction                 A time series consists of numerical data collected observed or recorded at more or less regular intervals of time each hour, day, month, quarter or year, More specifically, it is any set of data in which observation are arranged in a chronological order, Examples of time series are the hourly temperature recorded at a locality for a period of year, the weekly prices of wheat in Lahore, the monthly consumption of electricity in a certain town, the monthly total of passengers carried by rial,the quarterly sales of a certain fertilizer, the annual rainfall at Karachi for a number of year, the enrollment of students in a college or university over a number of year and so forth.               The analysis of a time series is a process by which a set of observation in a time series in analyses.Time series analysis is rather a difficult topic but we shall limit our discussion to the basics of time series analysis          The observation in a time series, d
Post a Comment
Read more

HEAT AND THERMODYNAMICS

By
U                        HEAT AND THERMODYNAMICS        Thermodynamics deals with various phenomena of energy and related properties of matter, especially the transformation of heat into other forms of energy. An example of such transformation is the process converting heat into mechanical work. Thermodynamics thus plays central role in technology, since almost all the raw energy available for our use is liberated in the form of heat. in this topic we shall their significance and applications.               KINETIC THEORY OF GASES       The behavior of gases is well accounted for by the kinetic theory based on microscopic approach. Evidence in favor of the theory is exhibited in diffusion of gases and Brownian motion of smoke particles etc.      The following postulates help to formulate a mathematical model of gases.      A finite volume of gas consists of very large number of molecules.      The size of the molecules is much smaller then the separation between molecules.
Post a Comment
Read more