1. Simple Harmonic Motion

2. Simple Harmonic Motion (SHM)
periodic motion about an equilibrium point where the restoring force is proportional to the distance from equilibrium
Periodic motion: Repeated motion
Equilibrium position: Position where object will come to rest. Fnet = 0
For oscillation to be SHM, the forces must always be directed to the center of symmetrical oscillation and the force must be proportional to the displacement.

3. Simple Harmonic Motion (SHM)
Examples:
Pendulum
Spring
Liquid in U-tube

4. SHM and Waves Simple Harmonic Motion- Pendulum Waves
Visualization_SHM_Pendulum
Visualization_SHM_BlockSpring
Visualization_SHM_LiquidInUTube

5. Simple Harmonic Motion (SHM)
Displacement vs. Time Graph
Sinusoid Wave Properties
period (T)
amplitude
displacement (m)
time (s)
frequency (f) = #cycles per second
midline = equilibrium position

6. Amplitude maximum displacement from equilibrium
Relates to the amount of energy
Unit: meters

7. Simple Harmonic Motion
pendulum (small angles)
mass on spring
amplitude = A
amplitude = A
equilibrium
equilibrium
amplitude = -A
amplitude = -A
equilibrium
equilibrium
amplitude = A
amplitude = A

8. Velocity / Force / Acceleration
At equilibrium
Velocity is at a maximum
Net force is zero
Acceleration is zero
At maximum amplitude
Velocity is zero
Net force is at a maximum
Acceleration is at its maximum

9. What happens as the pendulum moves?
At point D: equilibrium
At point A:
At point G:
Restoring force works to slow down bob, so it will return to equilibrium.

10. What happens as the pendulum moves?

11. Period & Frequency Period (T): time it takes to complete one cycle
Unit: seconds
Frequency (f): number of cycles or vibrations per unit of time
Unit: 1/sec = Hertz (Hz)

12. Example 1
An angry bird flaps its wings every 1.2 seconds. What is the period and frequency of the wings’ motion?

13. Example 1
An angry bird flaps its wings every 1.2 seconds. What is the period and frequency of the wings’ motion?