Simple Harmonic Motion

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Harmonic Motion

• Simple Harmonic Motion
• Spring and Pendelum (3 hrs)
• 1/05/07

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Harmonic Motion

• simple harmonic motion a physical phenomena
  that involves periodic motion. One example of
  such motion is provided by the action of Hookes
  Law.

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Harmonic Motion

• Springs Hookes Law
• Up to the elastic limit, the extension (x) of a
  spring is proportional to the tension force.
• F - k x
• where k spring constant
• (units are N m-1)
• x displacement

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Harmonic Motion

• According to Hookes Law, when an object
  stretches or compresses a spring from its
  equilibrium position, a restoring force always
  pushes the object back towards the equilibrium
  position. This causes the object to oscillate
  around the equilibrium point.

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Harmonic Motion

• Simple harmonic motion occurs when the net force
  along the direction of motion obeys Hookes law
  i.e. when the net force is proportional to the
  displacement from the equilibrium point and is
  always directed toward the equilibrium point.

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Harmonic Motion

• amplitude (A) the maximum distance of the
  object from its equilibrium position.
• period (T) time it takes the object to move
  through one complete cycle of motion from x A
  to x -A and back.
• frequency (f) the number of complete cycles or
  vibrations per unit time (f 1/T).

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Harmonic Motion

• Combining Newtons second law with Hookes law,
  we get an example of a harmonic oscillator
  equation.
• F - kx ma
• ? a -k x where A lt x lt A
• -----------
• m

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Harmonic Motion

• Remember that
• elastic PE
• ½ x (spring constant) x (displacement)2
• PESPRING ½ kx2

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Harmonic Motion

• Combining the equations for kinetic energy and
  elastic potential energy allows us to calculate
  the velocity of the object at any point in the
  oscillation. We can then combine use the
  velocity to calculate the period of the object.

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Harmonic Motion

• T 2p (m / k)-½
• or for a pendulum, the period is
• T 2p (L / g)-½
• where L is the length of the pendulum.

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Harmonic Motion

• End of
• Simple Harmonic Motion

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Ideal Gases

• Notes