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Oscillations

Oscillations. Objectives: (d) define simple harmonic motion ; (e) select and apply the equation a = – (2 π f ) 2 x as the defining equation of simple harmonic motion; (f) select and use x = A cos(2 π ft ) or x = A sin(2 π ft ) as solutions to the equation a = – (2 π f ) 2 x ;.

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Oscillations

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  1. Oscillations Objectives: (d) define simple harmonic motion; (e) select and apply the equation a = – (2πf)2x as the defining equation of simple harmonic motion; (f) select and use x = Acos(2πft) or x = Asin(2πft) as solutions to the equation a = – (2πf)2x ;

  2. Outcomes All Must Be able to define simple harmonic motion. Most Should Be able to select and apply the equation a = – (2πf)2x as the defining equation of simple harmonic motion; Be able to select and use x = Acos(2πft) or x = Asin(2πft) as solutions to the equation a = – (2πf)2x. Be able to explain why the period of an object with simple harmonic motion is independent of its amplitude;

  3. Oscillations • What is an oscillation? • An object oscillates when it moves repeatedly to and fro about a fixed point

  4. Representing oscillations • DEMO

  5. Representing oscillations • We have demonstrated how an oscillation can be described in similar terms to circular motion

  6. The Auxiliary Circle

  7. Phase • Two different masses released at the same time • Would be completely in phase with each other: • 0 degrees out of phase, 0 radians.

  8. Phase • Two different masses released at different times • Would be out of phase with each • other: ¼ of a cycle, 90 degrees out of phase, • or /2 radians.

  9. Phase • Two different masses released at different times • Would be completely out of phase with each • other: ½ a cycle, 180 degrees out of phase, • or  radians.

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