1. Simple Harmonic Motion and Wave Interactions
Physics – Chapter 12-1, 12-2
Simple Harmonic Motion and Wave Interactions

2. Wave Interactions (12-1) Simple Harmonic Motion A. Hooke’s law
- Periodic motion – a repeated motion
example: swinging on a swing, grandfather clock pendulum, mass on a spring

3.  When a spring with a mass is stretched or compressed and released the energy is also released and the spring-mass system vibrates back and forth in a periodic manner

4. Velocity is maximum at equilibrium position (x=0)
Spring force and acceleration reach their maximum at max displacement (x = 1 or x = -1)

5. In the absence of friction (damping) the mass-spring system would oscillate forever
The spring force pulls or pushes the mass toward equilibrium
 The restoring force

6. If the restoring force is proportional to the displacement then the motion is called simple harmonic motion
- Simple Harmonic Motion – vibration around an equilibrium position where restoring force is proportional to displacement
 will go back and forth over the same path

7. Hooke’s Law
Felastic = -k•x
x = displacement
 measured in meters
k = spring constant
 measured in Newtons/meter
F = spring force (elastic)
 measured in Newtons

8. The negative sign shows that the spring force is opposite in direction to the mass’ displacement and moves it towards equilibrium
This applies to a mass vibrating horizontally
If vibrating vertically, you must take gravity into account ( kx = -mg)
The system has elastic potential energy, which changes to kinetic and back again.

9. B. Simple Pendulums
- A mass (called a pendulum bob) attached to a
fixed string with negligible mass
- Can be approximated to a physical pendulum

10. 12-2 Measuring Simple Harmonic Motion
Simple harmonic motion – Vibration around an equilibrium point, in which displacement force = force pushing it back toward equilibrium

11. Amplitude – maximum displacement from equilibrium
Period (T) – time it takes for one full cycle of motion to occur
 measured in seconds (s)
Frequency (f) – number of cycles (vibrations) per second
 measured in Hertz (Hz)
1 Hertz = 1 cycle / second

12. * Period and frequency both involve time
f = 1/T T = 1/f
 Inversely related
* If you have one of the values, the other can always be calculated

13. Simple Pendulum
 Period depends on the string length and free-fall acceleration
*For small angles (<15o), amplitude and mass are not factors in a pendulum’s period

14. *Equations for pendulum and mass-spring system*