Oscillations Objectives: (d) define simple harmonic motion; (e) select and apply the equation a = – (2πf) 2 x 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) 2 x ;

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

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

Representing oscillations DEMO

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

The Auxiliary Circle

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

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.

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.