1. Chapter 12
Vibrations and Waves

2. Periodic Motion
Any repeated motion
Examples?

3. Describe velocity, force and acceleration at a, b and c
c is the equilibrium or rest position
The force is called the restoring force

4. Any periodic motion where the restoring force is proportional to the displacement is called simple harmonic motion
Frestore = -kDx

5. Felastic = -kx Hooke’s Law spring force
spring constant: how stiff the spring is
- because force is opposite displacement
x = displacement from rest position

6. I have a mass of 85 kg. I jump on a trampoline and it compresses 40 cm before propelling me up. What is the spring constant of the trampoline?
Felastic = Fweight
k = -F/-x
= 2085 N/m
Fweight = mg
Fweight = 834 N
x = 0.40 m

7. A pendulum moves in simple harmonic motion when displacement angles are small, less than 15°

8. Forces on a Pendulum Net Force? acceleration? velocity? Net Force?FT
velocity? FT
Fgy mg mg
Fgx

9. Time Measurements
Period, T, is the time for one back and forth motion in seconds
Frequency, f, is how often back and forth motions occur in 1 second, measured in hertz, Hz

10. Period of a Pendulum
Period only depends on L, the length of the pendulum

11. Period of a mass-spring system