oscillation and waves summary - IB PHYSICS SUBSIDIARY LEVEL...

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IB PHYSICS SUBSIDIARY LEVEL OSCILLATIONS AND WAVES SUMMARY 4.1 Kinematics of Simple Harmonic Motion (SHM) (2h) An oscillation is a small side to side movement of an object about its normal position. Displacement is the position of the object relative to its normal position. The amplitude is the greatest distance the object moves from its normal position. Frequency is the number of oscillations that occur in 1 sec. Period is the time to complete one oscillation. Phase is the fraction of a cycle one object is behind another when they both oscillate at the same frequency but not in time. The angular frequency of an oscillation is equal to 2 π divided by its period. When an oscillating object’s acceleration is in the opposite direction to its displacement and proportional to the size of its displacement, the object is performing Simple Harmonic Motion. For an SHM with angular frequency ϖ , amplitude r, maximum velocity v o : if displacement is -r when t = 0: x = -r cos ϖ t v o = ϖ r v = v o sin ϖ t if displacement = 0 when t = 0: x = r sin ϖ t v o = ϖ r v = v o cos ϖ t For any initial conditions, v = ± ϖ√ r 2 - x 2 4.2 Energy changes during simple harmonic motion (SHM) (1h) As an object performing SHM moves away from its mean position, the stored PE increases and the KE decreases. For amplitude r, when displacement is x the kinetic energy E k = ½ m ϖ 2 (r 2 – x 2 ), the total energy is E T = ½ m ϖ 2 r 2 and the potential energy is E P = ½ m ϖ 2 x 2 . 4.3 Forced oscillations and resonance (3h) Damping occurs when there is considerable opposition to an oscillation from an outside source. Damping transfers energy away from the object that is oscillating.
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