Periodic Motion Motions that repeat in a regular cycle.

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Periodic MotionMotions that repeat in a regular
cycle.
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Simple Harmonic Motion

• During motion, object has one point where the net
  force is zero (equilibrium).
• Whenever the object if pulled away from
  equilibrium, the net force becomes non-zero and
  works to pull the object back to equilibrium.
• The force needed to restore equilibrium is
  directly proportional to the displacement of the
  object.

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• Period (T) - time for the object to complete one
  cycle of motion.
• Amplitude - maximum distance that the object
  moves away from equilibrium.

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• Hookes Law - The force exerted by a spring is
  equal to the spring constant times the distance
  the spring is compressed or stretched from its
  equilibrium point. F -kx
• Potential energy in a stretched or compressed
  spring is equal to one half the product of the
  spring constant and the square of the
  displacement. PEsp ½ kx2

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Period of a Pendulum is equal to two times pi
times the square root of the length of the
pendulum divided by acceleration due to gravity.
T 2?vl/g
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Resonance - the increase in the amplitude of a
vibrating or oscillating object due to the
application of small forces during regular
intervals.

• Pumping your legs when swinging.
• Wind causing the Tacoma Narrows bridge collapse.

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Wave - a disturbance that carries energy through
matter or space (matter is not transferred).
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• Transverse Wave - wave pulse (disturbance)
  vibrates perpendicular to the direction of the
  waves motion.
• Longitudinal Wave - wave pulse (disturbance)
  vibrates parallel to the direction of the waves
  motion.

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Wave Measurements

• Speed (v) - the speed of a wave pulse is equal to
  the displacement of the wave peak divided by the
  amount of time. v ?d / ?t
• Amplitude (A) - the maximum displacement of the
  wave from its position of rest. For waves that
  have the same speed, the rate of energy transfer
  is proportional to the square of the amplitude.
• Wavelength (?) - the shortest distance between
  points where the wave pattern repeats itself.
• Period (T) - the time it takes wave to complete
  one cycle (wavelength).
• Frequency (f) - the number of complete
  oscillations it makes each second.

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• The frequency of a wave is equal to the
  reciprocal of the period. f 1 / T
• The wavelength is equal to velocity divided by
  the frequency. ? v / f

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Wave Behavior

• Incident wave - initial wave that strikes a
  boundary.
• Reflected wave - returning wave after the
  collision of the incident wave with a boundary.

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Principle of Superposition

• When two waves exist in the same place in the
  medium at the same time the displacement of the
  medium is equal to sum of the two individual wave
  displacements.

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Wave Interference - the result of the
superposition of two or more waves.

• Destructive - when two waves with opposite
  amplitudes meet. If these are equal amplitudes
  then the point that they meet (node) does not
  move.
• Constructive - when two waves with amplitudes in
  the same direction meet. Produces an a point
  where the largest amount of displacement occurs
  (antinode).

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• Standing waves are produced through the
  constructive and destructive interference of
  waves. Increasing the frequency of oscillations
  increases the number of nodes and antinodes.

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Waves in 2 Dimensions

• When an incident wave strikes a barrier it will
  be reflected. The angles formed between the
  incident ray and the normal (draw line that is
  perpendicular to the barrier) and the reflected
  ray and the normal are equal.

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• Refraction is the change in direction of a wave
  at the boundary between two different media.
• For example waves approaching shore will always
  have the same frequency, however, their
  wavelength and velocity decreases. This will
  cause a change in direction between these two
  media.