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Chapter 13: Oscillations About Equilibrium Whenever F = -kx or U(x) is a parabola

Chapter 13: Oscillations About Equilibrium Whenever F = -kx or U(x) is a parabola. F = -kx. U = kx 2 /2. Chapter 13: Oscillations About Equilibrium. Ch13-1 Periodic Motion T = period – the time for one cycle or repeat time f = frequency – the number of cycles per second f = 1/T

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Chapter 13: Oscillations About Equilibrium Whenever F = -kx or U(x) is a parabola

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  1. Chapter 13: Oscillations About Equilibrium Whenever F = -kx or U(x) is a parabola F = -kx U = kx2/2

  2. Chapter 13: Oscillations About Equilibrium Ch13-1 Periodic Motion T = period – the time for one cycle or repeat time f = frequency – the number of cycles per second f = 1/T  = angular frequency – radians per second  = 2f = 2/T Don’t confuse angular frequency with angular velocity.

  3. Chapter 13: Oscillations About Equilibrium Ch13-2 Simple Harmonic Motion (SHM)

  4. Chapter 13: Oscillations About Equilibrium Ch13-2 Simple Harmonic Motion (SHM) Displaying Position Versus Time for Simple Harmonic Motion x = Acos(2t/T) t = 0

  5. Chapter 13: Oscillations About Equilibrium Ch13-2 Simple Harmonic Motion (SHM) Simple Harmonic Motion as a Sine or a Cosine

  6. Chapter 13: Oscillations About Equilibrium Ch13-2 Simple Harmonic Motion (SHM) P13.8 (p.425)

  7. CT1: A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. At point P, the mass has • positive velocity and positive acceleration. • positive velocity and negative acceleration. • positive velocity and zero acceleration. • negative velocity and positive acceleration. • negative velocity and negative acceleration. • negative velocity and zero acceleration. • zero velocity but is accelerating (positively or negatively). • zero velocity and zero acceleration.

  8. CT2: A mass suspended from a spring is oscillating up and down as indicated. Consider two possibilities: (i) at some point during the oscillation the mass has zero velocity but is accelerating (positively or negatively); (ii) at some point during the oscillation the mass has zero velocity and zero acceleration. • Both occur sometime during the oscillation. • Neither occurs during the oscillation. • Only (i) occurs. • Only (ii) occurs.

  9. Chapter 13: Oscillations About Equilibrium Ch13-3 Connections Between Uniform Circular Motion and SHM

  10. Chapter 13: Oscillations About Equilibrium Ch13-3 Connections Between Uniform Circular Motion and SHM Position Versus Time in Simple Harmonic Motion

  11. Chapter 13: Oscillations About Equilibrium Ch13-3 Connections Between Uniform Circular Motion and SHM Velocity Versus Time in Simple Harmonic Motion

  12. Chapter 13: Oscillations About Equilibrium Ch13-3 Connections Between Uniform Circular Motion and SHM Acceleration Versus Time in Simple Harmonic Motion

  13. Chapter 13: Oscillations About Equilibrium Ch13-3 Connections Between Uniform Circular Motion and SHM P13.22 (p.425)

  14. P13.66 (p.428)

  15. Chapter 13: Oscillations About Equilibrium Ch13-4 The Period of a Mass on a Spring P13.63 (p.427)

  16. P13.31 (p.426) k m1

  17. Factors Affecting the Motion of a Mass on a Spring

  18. Chapter 13: Oscillations About Equilibrium Ch13-5 Energy Conservation in Oscillatory Motion E = mv2/2 + kx2/2 = kA2/2 = mvmax2/2 = mA22/2

  19. Chapter 13: Oscillations About Equilibrium Ch13-5 Energy Conservation in Oscillatory Motion U = kA2cos2t/2 K = mA22sin2t/2 = kA2sin2t/2

  20. Chapter 13: Oscillations About Equilibrium Ch13-5 Energy Conservation in Oscillatory Motion P13.67 (p.428)

  21. CT3: In P13.67b, which principle do we have to use to get the speed of the bob and bullet right after the collision? • Newton’s laws. • Conservation of energy. • Conservation of momentum. • The work-kinetic energy theorem.

  22. CT4: In P12.67b, which principle do we have to use to get the speed of the bullet from the height the bob rises? • Newton’s laws. • Conservation of energy. • Conservation of momentum. • The work-kinetic energy theorem.

  23. Chapter 13: Oscillations About Equilibrium Ch13-6 Simple Pendulum

  24. r t

  25. Chapter 13: Oscillations About Equilibrium Ch13-6 Simple Pendulum P13.67c (p.428)

  26. CT5: In P13.52a the acceleration of gravity at the surface of the Moon is one-sixth that at the surface of the Earth. If the pendulum were taken to the Moon, the period will • increase. • decrease. • stay the same.

  27. Simple Pendulum: Energy View

  28. Chapter 13: Oscillations About Equilibrium Ch13-7 Damped Oscillations

  29. Chapter 13: Oscillations About Equilibrium Ch13-7 Damped Oscillations

  30. Chapter 13: Oscillations About Equilibrium Ch13-8 Driven Oscillations and Resonance

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