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