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Hooke's Law and Simple Harmonic Motion
Who Was Robert Hooke
I have a special interest in Robert Hooke. On March 20th 1665 he published a book called "Micrographia" that explained his theories on microscopy and his invention of a new microscope. I work in the field of pathology and find the history of microscopy fascinating and I am excited to share a little about the history of this great scientist and his work on simple harmonic motion.
Robert Hooke was born on the 18th of July 1635 at Freshwater, Isle of Wight. In 1661 he published his first article on capillary attraction and became a Fellow of the Royal Society in 1663.
On the 9th of May 1664 Hooke logged down the rotations of Jupiter he also discovered the fifth star in the Orion Trapezium.
On July 1664 Hooke calculated the number of vibrations for each of the musical notes. This discovery relates directly to harmonic motion and will be discussed later. He also studied air in respiration and combustion, and the laws of falling bodies. He improved on the diving bell and telegraphy and invented a machine for cutting gear wheels.
At the same time of the publication of "Micrographia" Hooke drew a map of Mars and proved that the Earth and the Moon revolved around the sun in an elliptical pattern. He also published an observation of the Comet of 1664.
In 1666 Hooke played a major role in the engineering and rebuilding of London after the Great Fire.
In 1674 he published his principles of springs in "A Description of Helioscopes." Another important publication in the description of simple harmonic motion.
In 1678 he published an article on the Comet of 1677 and also his "Theories on Elasticity" which is on the kinetic theory of gases.
In 1700 he invented the Marine Telescope and died of complications due to diabetes on March 3rd 1703 at the age of 68.
Throughout his academic life he battled with Newton about many of his theories. It is interesting to point out that both had their hands in the great discoveries in Mathematics, Astronomy, and Physics that have changed our perception of the world.
Elastic materials return to their original form after being deformed. The elasticity of an elastic material is the restoring force on the material after deformation.
Most elastic materials have a restoring force proportional to the amount of deformation. This applies only if the deformation is not too great. In a stretched spring the restoring force is equal to the distance in which the spring stretches.
The equation that shows this is called Hooke's Law and appears as follows:
F = Restoring Force
k = Constant of Proportionality or the Spring Constant
x = Distance from One End of the Spring to the Stretched End
The Spring Constant, k, shows how much stiffness is in the spring the stiffer the spring the larger the Spring Constant.
The Spring Constant depends on the radius of the wire in the spring, the radius of the coils of the spring, and the number of coils in the spring.
The negative sign in the equation is there because the (k)(x) value is opposite the restoring force.
When a motion of an object is repeated in intervals it is called periodic motion, for example a pendulum.
A particle or object in motion under the influence of a restoring force is described as simple harmonic motion.
Simple harmonic motion is a periodic oscillation that is commonly found in nature. For example the vibrations of musical notes.
If you graph the results obtained from Hooke's apparutus the graph would resemble a wave with crest and trough. Simple Harmonic motion is named due to the restoring force of the spring making the periodic motion simple and the cos and sin of the resulting crest and trough of the wave created has a harmonic function.
This wave is similar to waves seen on plucked strings or in disturbed water. Hooke's law and simple harmonic motion help to describe waves and how they operate.
Not only is the law helpful in the explanation of waves but also in a discussion of how springs are created and operate.
So with a large smile we should thank Hooke for all he has done, since without him we may not have pushed that Slinky down the stairs years ago.