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Oscillations

Oscillations. Monday, November 19 Lecture 30. Workbook problems due Wednesday. WB 10.5, problems 14-25. Workbook Problems due Fri day. Problems 14-1 through 8, pages 14-1 -- 5. Power. Power is the rate of transformation of energy Unit is 1 Watt=1W = 1 J/s

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Oscillations

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  1. Oscillations Monday, November 19 Lecture 30

  2. Workbook problems due Wednesday • WB 10.5, problems 14-25

  3. Workbook Problems due Friday • Problems 14-1 through 8, pages 14-1 -- 5

  4. Power • Power is the rate of transformation of energy • Unit is 1 Watt=1W = 1 J/s • If energy being transformed is work, W then

  5. Is the work done by F + or - ? • Positive • negative F d

  6. Is the work done by F + or - ? • Positive • negative F d

  7. Is the work done by F + or - ? • Positive • negative F d

  8. Problem 10:20 • A pendulum is made by tying a 500g ball to a 75-cm-long string. The pendulum is pulled 300 to one side and then released. • A) What is the ball’s speed at the lowest point in its trajectory? • B) To what angle does the pendulum swing on the other side.

  9. Problem 10:20 • Use energy conservation L=0.75 m 300 Δy=L-Lcos 300

  10. Problem 10:20 cont • Set y=0 at lowest point of swing

  11. Problem 10:24 • A student places her 500g physics textbook on a frictionless table. She pushes the book against a spring 4.00cm and then releases the book. What is the book’s speed as it slides away? The spring constant is k = 1250 N/m.

  12. Problem 10:24 • A student places her 500g physics textbook on a frictionless table. She pushes the book against a spring 4.00cm and then releases the book. What is the book’s speed as it slides away? The spring constant is k = 1250 N/m.

  13. Problem 10:24 • Using the initial position as the compressed spring, final after book leaves spring:

  14. Problem 10:24 • Finally

  15. Equilibrium and Oscillation • Frequency and Period

  16. Simple Harmonic Motion • Linear restoring force— • Example, mass on a spring • Set y=0 at equilibrium point:

  17. Simple Harmonic Motion • If restoring force is linearly proportional to displacement (e.g. F=-kx) then we will have simple harmonic motion. • In lab last week you experimented with a simple pendulum. Was its motion simple harmonic?

  18. θ T w cosθ w sin θ w

  19. Simple Pendulum Find the angular frequency is

  20. Description of motion

  21. At what time(s) is particle moving right at maximum speed? • At what time(s) is particle moving right at maximum speed? • At what time(s) is the speed zero?

  22. Problem 14:7 An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0s. It then oscillates with T=2.0s and vmax = 40cm/s A=? x(t=0.25s) = ?

  23. Problem 14.7

  24. Wednesday Oscillations continued Problems CQ3,CQ9,MC18,MC19, 1, 4, 6, 7, 10

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