Simple Harmonic Motion another way of describing waves

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Simple Harmonic Motion(another way of describing
waves)

• Periodic Motion
• Motion that repeats itself at regular time
  intervals
• Simple Harmonic Motion
• Specific type of periodic motion
• Motion is sinusoidal (like a sine wave)
• Movement traces out a sine (or cosine) curve
• All SHM is periodic, but not all periodic motion
  is SHM

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What makes motion harmonic?

• Two conditions must be met
• There must exist an equilibrium position if
  the system is placed at this position, it will
  not move
• A linear restoring force must be present a
  force that always pushes the system back toward
  equilibrium
• The further away the system is from
  equilibrium, the stronger the force

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One example, a weight on a spring
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Components of SHM

• The amplitude (A) is how far the maximum
  displacement is from equilibrium
• The period (T) is how long it takes to make one
  oscillation.
• The frequency (f) is how many oscillations there
  are per second, having units of hertz (Hz)
• They are inverses of each other
• f 1/T
• T 1/f

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Force in SHM

• Because the spring force always tries to push or
  pull the mass back to an equilibrium position, it
  is sometimes called a restoring force.

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Hookes Law

• In 1678, Robert Hooke found that most mass-spring
  systems (not all) have a specific relationship
  between force and displacement.
• For small displacements from equilibrium we can
  say
• Felastic -kx
• Felastic spring force
• k spring constant
• x displacement

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Specifics

• The negative sign signifies that the force of the
  spring is always acting in the opposite direction
  as the displacement.
• Units for k are N/m

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Period of a Spring-Mass System

• Period of a mass-spring system depends on mass
  and spring constant

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Velocity in SHM

• In simple harmonic motion, the velocity
  constantly changes, oscillating just as the
  displacement does.
• When the displacement is maximum, however, the
  velocity is zero
• When the displacement is zero, the velocity is
  maximum.
• spring animation

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A Simple Pendulum

• A simple pendulum is one which can be considered
  to be a point mass (bob) suspended from a string
  or rod of negligible mass.

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• The restoring force of a pendulum is a component
  of the bobs weight.
• In an AP or college Physics course, we would use
  trigonometry to calculate the force pulling on
  the bob.

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Transformation of Energy in a Pendulum

• PE increases as the pendulums displacement
  increases.
• KE increases as the PE decreases
• simulator

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Period of Pendulum

• The period depends on the string length and
  free-fall acceleration.
• For small amplitudes, the period of such a
  pendulum can be approximated by

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Why?

• Length of String
• Different length, but same amplitude and mass,
  shorter length will have a smaller arc to travel
  through.
• Because the distance the mass travels from
  maximum displacement to equilibrium is less,
  while the acceleration is the same (gravity acts
  the same on both identical masses), the shorter
  pendulum will have a shorter period

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Lab Make your own clock

• You will use your new knowledge of pendulums to
  make a simple clock.
• Your lab report will consist of
• Instructions for measuring time with your clock
• Explanation of how your clock works with all
  calculations
• Percent difference calculations comparing your
  clock to my stopwatches
• This formula is on page 100 of your workbooks