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Measuring Simple Harmonic Motion

Measuring Simple Harmonic Motion. Chapter 12 Section 2. Measuring The Motion . There are 3 things that determine the motion of a mass in simple harmonic motion. Amplitude Period Frequency. Amplitude. Amplitude – The maximum displacement from the equilibrium position.

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Measuring Simple Harmonic Motion

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  1. Measuring Simple Harmonic Motion Chapter 12 Section 2

  2. Measuring The Motion • There are 3 things that determine the motion of a mass in simple harmonic motion. • Amplitude • Period • Frequency

  3. Amplitude • Amplitude – The maximum displacement from the equilibrium position. • Can be measured in different ways • Pendulum – The angle (radians) between the equilibrium position and the maximum displacement. • Spring-mass – The maximum amount (meters) stretched or compressed from the equilibrium position.

  4. Period • Period – The time it takes to execute a complete cycle of motion. • For example: • If it takes 5 seconds for a person on a swing to swing back and forth, then the period of the motion would be 5 seconds. • SI units for period – Seconds (s) • Variable given for period – Capital letter (T)

  5. Displacement For Period • The displacement of an object in simple harmonic motion during the time of 1T (time to compete one cycle) is “ZERO.”

  6. Frequency • Frequency – The number of cycles or vibrations per unit time. • For example: • The person on the swing completes one cycle in 5 seconds, the frequency would be 1/5 cycles per second or 0.2 cycles per second.

  7. Units For Frequency • SI units for frequency – S-1 • This is known as Hertz (Hz) • Variable for frequency – lower case letter (f) • In the case of the person swinging, the frequency would be: • 0.2 cycles per second = 0.2 Hz • A typical TV set has a frequency of 60Hz, which means 60 frames per second.

  8. Differences Between Period and Frequency • Period is time per cycle. • Frequency is the number of cycles per unit time. • They are inversely proportional.

  9. Equations For Frequency and Period • If the period or the frequency is known, this relationship can be used to calculate the other value. • Period (s) • Frequency (Hz)

  10. Determining The Period of a Pendulum • The strings length and the free fall acceleration determine the period of a simple pendulum. • Things that don’t determine the Period: • Amplitude (for angles less then 15 degrees) • Mass of the bob

  11. Simple Pendulum Equation

  12. Example Problem #1 • A desktop toy swings back and forth once every 1.0 seconds. How tall is this toy?

  13. Example Problem #1 Answer • length = 0.25m

  14. Example Problem #2 • What is the period of a 3.98m long pendulum?

  15. Example Problem #2 Answer • T = 4.00 seconds

  16. Period of a Mass-Spring System • The mass attached to the spring and the spring constant (k) determine the period. • Things that don’t determine the period: • Amplitude

  17. Period of a Mass-Spring System Equation

  18. Example Problem #3 • A 1.0 kg mass attached to one end of a spring completes one oscillation every 2.0 seconds. Find the spring constant.

  19. Example Problem #3 Answer • k = 9.9N/m

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