10_1425_web_Lec_28_SimpleHarmonicMotion

10_1425_web_Lec_28_SimpleHarmonicMotion - Simple Harmonic...

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Simple Harmonic Motion Physics 1425 Lecture 28 Michael Fowler, UVa
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Force of a Stretched Spring If a spring is pulled to extend beyond its natural length by a distance x , it will pull back with a force where k is called the spring constant ”. The same linear force is also generated when the spring is compressed . A Natural length F kx = − Extension x F kx = − Spring’s force
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Mass on a Spring Suppose we attach a mass m to the spring, free to slide backwards and forwards on the frictionless surface, then pull it out to x and let go. F = ma is: A Natural length m Extension x F kx = − Spring’s force m frictionless 22 / md x dt kx = −
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Solving the Equation of Motion For a mass oscillating on the end of a spring, The most general solution is Here A is the amplitude, f is the phase, and by putting this x in the equation, m ω 2 = k , or Just as for circular motion , the time for a complete cycle 22 / md x dt kx = − ( ) cos xA t ωφ = / km ω= 1/ 2 / 2 / ( in Hz.) T f mk f πω π = = =
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Energy in SHM: Potential Energy Stored in the Spring Plotting a graph of external force F = kx as a function of x , the work to stretch the spring from
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This note was uploaded on 12/07/2011 for the course PHYSICS 1425 taught by Professor Michaelfowler during the Spring '10 term at UVA.

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10_1425_web_Lec_28_SimpleHarmonicMotion - Simple Harmonic...

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