OscillationsObjectives:

(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 ;

OutcomesAll 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.