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Lesson_5.1a_Printable - Oscillations If a loaded spring is...

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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 The rest position of the load is called its equilibrium position called an oscillation . 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 The compressed spring has potential energy and it does work pushing the load back to the equilibrium position giving it spring. equilibrium Lower extreme 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
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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 x 0 Upper Extreme K = 0, U 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 Lower Extreme A U = 0, K max 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 ). x 0 Upper Extreme We will now obtain an equation for the displacement y as a function of time. Equilibrium Lower Extreme http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMe chanics/SHM/TwoSHM.html A -A 4
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A θ B BC is a diameter of the circle. O A perpendicular drawn from Q meets BC at O . 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 C 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. through an angle θ . 5
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A θ B O y P Q When the object is at B, the projection O also is at B. y now equal to A , the radius of the circle. What is the value of angle θ when the object is at B? When θ increases from 0 to π /2 , the displacement y increases from 0 to A What happens to y as θ increases further in C the second quadrant?
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