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CHapter11

CHapter11 . Section 2 solving simple harmonics. Objectives. Identify the amplitude of vibration. Recognize the relationship between period and frequency. Calculate the period and frequency of an object vibrating with simple harmonic motion. Amplitude.

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CHapter11

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  1. CHapter11 Section 2 solving simple harmonics

  2. Objectives • Identify the amplitude of vibration. • Recognize the relationship between period and frequency. • Calculate the period and frequency of an object vibrating with simple harmonic motion.

  3. Amplitude • In the absence of friction, a moving trapeze always returns to the same maximum displacement after each swing. • The amplitude is the maximum displacement from equilibrium.

  4. Periods and frequencies • The period (T) is the time (in seconds) it takes for one complete cycle of the motion. • The SI unit of period is seconds (s). • The frequency ( f ) is the number of complete cycles that occur in one second. • The SI unit of frequency is s-1, which is called a hertz (Hz).

  5. Periods and frequencies • Period and frequency are inversely related: Since frequency is cycles per second and since period is seconds per cycle, frequency and period are reciprocals of each other:

  6. Measuring of simple harmonics

  7. Period of a simple pendulum • The period of a simple pendulum depends on the length and on the free-fall acceleration. • The period does not depend on the mass of the bob or on the amplitude (for small angles).

  8. Example 1 • An orangutan on a swing swings in simple harmonic motion with a period of 4.2 s. Calculate the length of the cables supporting the swing.

  9. Example 2 • You need to know the height of a tower • But darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12s. How tall is the tower.

  10. Student guided practice • Do problems 1-3 in your book page 375.

  11. Period of mass system • The period of an ideal mass-spring system depends on the mass and on the spring constant. • The period does not depend on the amplitude. • This equation applies only for systems in which the spring obeys Hooke’s law.

  12. Example • The body of a 1275kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153kg. When driven over a pothole in the road the frame vibrates with a period of 0.840s. Find the spring constant of a single spring.

  13. Student guided practice • Do problems 1-2 in your book page 377.

  14. homework • Do worksheet problems 1-5

  15. closure • Today we learned about period and frequency • Next we are going to learn about waves

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