This text is meant to accompany class discussions. It is not everything there is to know about simple harmonic motion. It is meant as a prep for class.
An oscillation is a back-and-forth motion like a playground swing, or a car that bounces up and down after hitting a hole in the road. There are 3 types of oscillations.
Forced oscillations
This is where a force is applied in rhythm with an oscillation. Pushing a child on a swing is a good example of this. The applied force increases the height of the swing's motion. Another example occurred when the wind blew through the canyon and caused the Tacoma Narrows Bridge to swing wildly.
This video is a little long but it tells an sad, and true, story about the car on the bridge and its passenger.
In case you are thinking that we learned our lessons about building bridges where high winds blow, guess again. This is a video, taken in May of 2010, is of a bridge near the city of Volgograd,in Russia.
Damped oscillations occur when a force is applied to stop the back-and-forth motion.
Here's an animated example that is actually a companies logo. The logo is dropped onto a platform, The platform quickly stops bouncing due to the combination of springs and shocks. (This same system is used on your car to keep it from bouncing.)
Earthquakes have to be considered in Japan when designing and building skyscrapers. One of the neatest innovations is a 800 ton motion damper built inside of the 101 story skyscraper called "Taipei 101." Below is a video of this damper during an Earthquake in 2008. This damper is about 90 floors above the ground. It sways out of sync with any building sway.
This video can be found on YouTube at, http://youtu.be/ohKqE_mwMmo. When an earthquake hits or high winds hit the side of the structure, the skyscraper will sway -alot. This damper sways out of rhythm with the swinging of the building to stop the vibrations more quickly.
If you are interested, here is a short video, shot from another building, showing these skyscrapers swaying in an earthquake, http://youtu.be/301b5aeWpjU.
Simple Harmonic Motion
Simple Harmonic Motion, shm, occurs when a object swings back-and-forth without any outside forces other than the "restoring force." Every body that swings, moves with its own period or frequency. This natural frequency is called the resonant frequency. The restoring force moves a body that is swinging, back towards its equilibrium position. The restoring force is also linear.
The arrow shows the direction of the
spring's restoring force. Notice how it always points towards the equilibrium position. What you can't is the fact that
it disappears as the equilibrium position
the restoring force is linear. But the previous page showed how the restoring force was linear.
The restoring force also changes in size with the motion of the block. It was also shown on the previous page that the greater the displacement from equilibrium the greater the force.
All simple harmonic motions' periods can be described by
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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