1. Chapter 11 Vibrations and Waves

2. Simple harmonic motion Measuring simple harmonic motion Properties of waves Wave interactions

3. Simple Harmonic Motion

4. SHM simple harmonic motion = vibration/oscillation about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium damping = the effect of friction on a mass-spring system that eventually brings the system to rest

5. Mass and Spring System Identify max & min: Force Acceleration Speed

6. Hooke’s Law

7. Practice If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

8. Simple Pendulum Identify the restoring force SHM for small angles only ( θ < 15° )

9. Simple Pendulum Identify max & min: Force Acceleration Speed

10. Energy What types of energy are transferred in each type of SHM?

12. Measuring SHM

13. Period of a Simple Pendulum

14. Practice A desktop toy pendulum swings back and forth once every 1.0 s. How long is this pendulum? What is the free-fall acceleration at a location where a 6.00 m long pendulum swings through exactly 100 cycles in 492 s? By what factor should the length of a pendulum be changed to double the period of the vibration?

15. Period of a Mass-Spring System

16. Practice A 1.0 kg mass attached to one end of a spring completes one oscillation every 2.0 s. Find the spring constant. A mass attached to a spring of spring constant 35 N/m makes 32 complete vibrations in 4.0 s. Find the mass.