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SIMPLE HARMONIC MOTION

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 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

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