Still continuing our discussion about motion, this time we are leaving Newton's laws for a moment. We want to talk about a very important type of motion in physics called Simple Harmonic Motion (SHM). This type of motion is really seen in many objects and gadgets in the world around us. So it is important to understand this type of motion. So what is Simple harmonic Motion?
Here is a definition that is very accurate.
a special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position source
So a simple harmonic motion is a type of periodic motion where an object suspended from a fixed position moves through and fro along a straight line towards the rigid position from where it is suspended and beyond it. To understand a simple Harmonic motion very one, one needs to define and properly understand certain elements of this type of motion. So lets consider them one after the other.
1. Fixed Position: In simple harmonic motion, the objects motion starts and is controlled from a fixed position. This position exerts some displacement and returning force, causing the motions motion to be about its equilibrium position. In practice, an object attached to a string motions towards the position where the string is tied to a stationary rigid body.
2. Periodic motion: By periodic motion, it means that the object is moving along a straight or circular line through and fro. The motion is repeated relative to the objects fixed point where the returning force acts.
The period in any Simple Harmonic motion can be measured in time and is defined as the total time it takes the object to make one complete revolution about its equilibrum.
To calculate the Period or time taken to complete one revolution, the formular used is T =n/t where
T = Period of motion
n = number of revolutions
t = total time taken.
3. Frequency: This is used to define the number of complete motions made by the object in a second. The frequency is just a reciprocal of the Period of motion for that object.
Having established that Period T = t/n, then, the Frequency F = 1/T. The SI unit of frequency is Hertz (Hz)
4. Amplitude: The amplitude of an object performing a simple harmonic motion is the farthest distance it attempts during the motion from its equilibrium. Usually, the amplitude happens during the first displacement when the object still has maximum force for its first revolution. The more revolution it makes, the weaker the force exacted from the rigid support. So amplitude is usually achieved when the force is strongest - always in the first revolution.
There are many different instances of Simple harmonic Motion. It includes the following:
Simple Pendulum: Simple pendulums are made up of a mass attached to a string at the lower end of it. The upper end of the string is tied to a rigid body such as a tree to provide equilibrium or support. When the mass is displaced over a small distance away from the rigid support, it performs simple harmonic motion.
Balance wheel of a watch: The balance wheel of a clock moves around a rigid support. As it revolves, it indicates the time and continues to make this periodic motion endlessly.
Loaded test tube in water: If a test tube is loaded with a weight and placed in a fluid like water, it can perform a simple harmonic motion when displaced. Its vertical oscillation is done around an equilibrium point in the water and things motion continues to happen up and down. That is a simple harmonic motion.
A child's swing: A child's swing consists of a seat with a rope tied to the seat. The other end of the rope is tied to a tree. When the child is seated and the swing displaced, it moves along a straight line in a repetitive circle, its returning force is around the equilibrium point. To maintain the endless revolution of the swing, a person might push the swing when its force is dying out.
Now we will look at one or two examples of how to solve for Period and frequency of a Simple harmonic Motion.
Example 1: A swing makes 120 revolutions in 30 seconds. What is the period and frequency of the swing?
**Solution:
Period T = t/n
T = 30/120
T = 0.25s.
Frequency f = 1/T
f = 1/0.25
f = 4 Hz
Simple Harmonic motion has a broad application in the world of Physics as it is used to understand how objects suspected from a fixed position make their revolution. A great understanding of this principle has led to the development of wrist watches and other devices.
