11-2%20:%20Measuring%20SHM

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11-2 Measuring SHM
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Amplitude, Period, and Frequency

• Amplitude the maximum displacement from the
  equilibrium position.
• Amplitude is given in radians or meters.
• Period the time it takes to execute a complete
  a full cycle of motion.
• Period(T) is given in seconds.

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• Given a certain unit of time, the frequency is
  given by the number of complete cycles that occur
  in that amount of time.
• Frequency symbol funit Hertz (Hz).
• Frequency and period are inversely related
• f T-1

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Period of a Simple Pendulum

• Depends only on the string length and the
  acceleration due to gravity.

T Period LLength of string gFree-fall
acceleration
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Period of a Mass-Spring System

• With a mass-spring system, mass does have an
  effect on the period.
• as mass increases, the period also increases.
• The greater the spring constant(k), then the
  higher the force that is required to stretch or
  compress the spring, thus a higher acceleration,
  which would bring a smaller period.
• Therefore, the higher the spring constant, the
  smaller the period.

TPeriod mMass kSpring Constant
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Sample Problem

• You desire to find the height of a small-model
  skyscraper so you attach a pendulum to the
  ceiling and it takes 15 seconds for the pendulum
  to return to the equilibrium location. How tall
  is the tower?

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Sample Problem (solved)

• t 15 seconds g9.81 m/s²
  L?

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Sample 2

• A pendulum makes 11 oscillations in 12 s. Find
  its period and frequency. Also find its period on
  Jupiter if the accel. due to gravity is 24.8
  m/s2.
• Given
• t 12 s
• of cycles 11

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• f of cycles/ time 11/12s 0.92 Hz

T f-1 1/0.92 Hz 1.09 s
On earth,
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• On Jupiter