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Simple Harmonic Motion

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by

JunWei Ren

on 21 January 2014

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Transcript of Simple Harmonic Motion

Simple Harmonic Motion
Galileo's discover
Galileo discovered the crucial property of pendulums: the period of the pendulum is neither depends on the amplitude nor depends on the mass of the bob. He also found that the period is proportional to the square root of the length of the pendulum.
An object on the end of a spring
Vibrating strings on a guitar
A pendulum
Conclusion
What is Simple Harmonic Motion
Simple harmonic motion is a periodic motion that vibrates or oscillates back and forth over the same path.
How is SHM graphed ?
What is the necessary condition for SHM
It must be
Periodic motion
Move back and forth
Over the same path
SHM in pendulums
Resources
Why are pendulums used in clocks
The advantage of a pendulum for timekeeping is that it is a harmonic oscillator; it swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates.
Examples
Hooke's Law
When a spring is compressed or stretched from its natural length, a force is created. If the spring is displaced by X from its natural length, the force it exerts in response is given by the equation
F = -kx
The spring tries to restore the attached ball to the equilibrium position. For this reason, we say that the spring provides a restoring force.
Displacement vs Time
Velocity vs. Time
At the endpoints of the oscillation region, the acceleration is maximized and it is zero at the equilibrium position.
SHM is periodic motion that move back and forth. (Ex. spring, pendulum,guitar)
F=-kx (Hooke's law)
The period of the pendulums is not depends on amplitude and mass.
Pendulum clock is more precise.
At the end of oscillation region : the object have zero velocity, maximum PE
At the equilibrium position: the object have zero acceleration and maximum KE.
Picture credits
http://farside.ph.utexas.edu/teaching/315/Waves/img28.png
http://www.themarkofaleader.com/wp-content/uploads/2012/07/Three-Chords.jpg
http://images.tutorvista.com/content/wave-motion-sound/simple-pendulum.gif
http://www.antonine-education.co.uk/Salters/BLD/graph.gif
http://www.tltgroup.org/images/Eqn_Simple_Harmonic_Motion.gif
http://www.seikoclocks.com/media/catalog/product/cache/1/image/800x800/9df78eab33525d08d6e5fb8d27136e95/q/x/qxc213b-large1024.jpg
http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0011/pendulum_summary.gif

Websites used
http://en.wikipedia.org/wiki/Pendulum_clock
http://en.wikipedia.org/wiki/Pendulum#1602:_Galileo.27s_research

Reference book used
Physics textbook
The Princeton Review AP Physics B guide book

By Devyn Lewis, Junwei Ren, Zhenni Ren
Full transcript