Simple Harmonic Motion

Let us start by a brief description on what SHM ( Simple Harmonic Motion ) . The motion of a particle moving along a straight line with an acceleration which is always towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point is called simple harmonic motion.

You are familiar with many examples of repeated motion in your daily life. If an object returns to its original position a number

of times, we call its motion repetitive. Typical examples of repetitive motion of the human body are heartbeat and

breathing. Many objects move in a repetitive way, a swing, a rocking chair, and a clock pendulum, for example. Probably

the first understanding the ancients had of repetitive motion grew out of their observations of the motion of the sun and

the phases of the moon.

A Scotch yoke mechanism can be used to convert between rotational motion and linear reciprocating motion. The linear motion can take various forms depending on the shape of the slot, but the basic yoke with a constant rotation speed produces a linear motion that is simple harmonic in form.


Everything! You name it, it will resonate in whole or part in some way. Auto suspension bounces, bridges sway, musical instruments vibrate, radio circuits resonate, clocks use a pendulum or a piezo electric crystal that resonates, walls, floors and columns resonate, etc. In most cases, we have to be sure that the Resonance Q factors are low so that the SHM is well damped, such as the use of shock absorbers in a car, ie we have to make things resonate as little as possible.


Let us understand the concept further more by a example problem.

Problem :

Suppose we are given a normal problem in which we have to and the energy of the spring: "A mass of 2 kg oscillating on a spring with constant 4 N/m passes through its equilibrium point with a velocity of 8 m/s. What is the energy of the system at this point? From this answer derive the maximum displacement, x of the spring? In this we are going to use the concept of di erential equation?

When the mass is at its equilibrium point, no potential energy is stored in the spring. Thus all of the energy of the system is kinetic, and can be calculated easily:

K = (1/2)m*v*v = (1/2)(2)(8)(8) = 64Joules

Since this is the total energy of the system, we can use this answer to calculate the maximum displacement of the mass.When the block is maximally displaced, it is at rest and all of the energy of the system is stored as potential energy in the spring .

Since energy is conserved in the system, we can relate the answer we got for the energy at one position with the energy at another:

(1/2)*m*8*8=m*g*x

(1/2)*8*8=10*x

x=3.2 meters

We used energy considerations in this problem in much the same way we did when we rst encountered conservation of energy- whether the motion is linear, circular or oscillatory, our conservation laws remain powerful tools.

Practical Application :

We can observe so many practical application of this problem all around us .The paradox poses a problem for us to all to and fro motion happens in this universe .Hence we analyse the practicality of a motion i.e to and fro taking place all around us.Some real life examples are "The string of a guitar" , "The pendulum of our grandfathers clock" , "the motion of our ear drum when it hears any type of sound" etc.

Conclusion :

Hence from the above mathematical problem we can conclude that the aplication is used by in many applications such as running of turbine,producing energy , designing automobiles,etc