# Vibratory Motion

Vibratory Motion

By Eugene Toth

Vibratory motion, or vibration differs from rotational motion and linear motion.  In vibration, motion progresses alternately changing direction at fixed intervals.

In the 6th century, the Greeks first studied vibration when they plucked the strings of instruments.   Pythagoras of Samos in Greece studied the relationship of vibrations to music.  People know Pythagoras of Samos better for discovering the Pythagorean Theorem (a2+b2=c2) in a triangle. The word vibration comes from the Latin word “vibrationis” for shaking.

shows many examples of vibratory motion.  Even humans experience vibrations. We can apprehend sound from instruments. Vibratory motion also encompasses sound. Since vibrations have relationship to music, vibratory motion is also known as harmonic motion.

We can’t distinguish some vibrations. Scientists call detectable sounds an example of “simple harmonic motion.”

Robert Hooke’s law pertains to simple harmonic motion.  In 1660, Hooke wrote that the extension of a string is the same as the force extending it. He wrote in his book:

“Ut tensio, sic vis”

meaning “as the extension, so the force.”  Vibration depends on elasticity.  If one pulls an elastic string to the right, it will rebound to the left with equal force.  Acceleration of an object must stop at a midpoint. The object maintains velocity.  Therefore, the object moves past the position of equilibrium.

In simple harmonic motion, velocity changes not abruptly, but smoothly at all times.  As the string passes the point of equilibrium, a restoring force comes into effect exerting a counter or negative acceleration until the velocity is cancelled out.  The string comes to a halt again back on the original side.  The restoring force now pushes the string back. Since the string has kinetic energy, it can’t stop.  As the string vibrates back and forth, air resistance and friction slow the string down down until it stops moving.  In theory, if air resistance and friction did not exist, the string would continue vibrating indefinitely.

Viscosity defines how at what speed a substance flows.  Water with low viscosity will flow quickly.  Honey with high viscosity flows slowly.  We find viscosity in any liquid.  Imagine the Earth, however, as a sphere with mass but no viscosity. Then, imagine we drop an object from the planet’s surface. The object begins to accelerate at 9.8 meters per second/second. As passes through the mass of the Earth and descends toward the center, the pull of gravity in the center depends on the core’s mass above it. Acceleration slows until the ball reaches the center of the Earth. At the center of the Earth the ball reaches maximum velocity. The ball continues through the center of the Earth and climbs up the Earth to the opposite side.

As the ball climbs up the other side of the Earth, gravity pulls the ball back to Earth. The ball continues climbing, slows as approaches the surface of the Earth. When It reaches the other side of the Earth, it stops. The force of gravity neutralizes the force of momentum. The ball then begins to drop back to the center of the Earth with increasing velocity but reducing acceleration. The ball passes back through the Earth’s center. The ball’s speed reduces until it returns to where it began. The process of the ball falling back and forth through the center of the Earth would repeat itself over and over again.

The ball falling through the center of the Earth shows an example of simple harmonic motion.  The ball moving back and forth through the center of the Earth represents vibrations.

The period of vibration is the time that it requires for the string to go from one side of the midpoint of the string’s travel and back.  Physicists call the time taken to compete this motion the period of motion.

Conclusion

Without air resistance and gravity, vibrations could continue forever.  A pendulum once launched could swing back and forth indefinitely.  A musical note, once sounded, could resound until the end of time.

## 2 thoughts on “Vibratory Motion”

1. omarabdelhamid

Awesome post! I’ll put it into the portfolio as soon as I get off vacation.

2. supermathgenius

for some reason, this makes me want to play my guitar cause I always just play a string to see it vibrate XD