Lesson 5.1a Oscillations

Lesson 5.1a Oscillations - Oscillations If a loaded spring...

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Oscillations If a loaded spring is pulled down and released, the system moves up and own about its equilibrium position. This up and down motion of the load is called an oscillation . The rest position of the load is called its equilibrium position When the load is pulled down to a lower extreme , the work done in stretching the spring becomes potential energy of the spring which pulls the load back to the equilibrium position. 1

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The kinetic energy at the equilibrium position does work compressing the spring so that the load moves to the upper extreme , compressing the spring. equilibrium Lower extreme The compressed spring has potential energy and it does work pushing the load back to the equilibrium position giving it kinetic energy. The spring has potential energy when the load is at either extreme. The load is at rest at the extremes and its kinetic energy is zero. 2
At the equilibrium position, the potential energy of the spring is zero. The load has maximum kinetic energy at this position. The amount of stretch of the spring from its equilibrium position is called the displacement (y) of the load. The maximum displacement of the load from the equilibrium position is called the amplitude (A) of the oscillation. Equilibrium Upper Extreme Lower Extreme A U = 0, K max K = 0, U max K = 0, U max 3

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As the load oscillates between the two extremes, its displacement y changes reaching a maximum at the upper extreme ( y = A ) and a minimum at the lower extreme ( y = -A ). We will now obtain an equation for the displacement y as a function of time. Equilibrium Upper Extreme Lower Extreme http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMe A -A 4
A θ B C BC is a diameter of the circle. O A perpendicular drawn from Q meets BC at O . O is called the projection of Q onto BC If the center of the circle is the origin, when the object is at P , the projection O is at the origin. When the object is at Q , the projection O moves up. y , the distance it moves up is called the displacement of the projection. y P Q Consider an object moving around a circle of radius A . At t = 0, the object is at P. A little while later, the object is at the point Q so that the radius rotates through an angle θ . 5

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A θ B C O y P Q When the object is at B, the projection O also is at B.
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson 5.1a Oscillations - Oscillations If a loaded spring...

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