1. Simple Harmonic Motion

2. What is an Oscillation? Vibration
Goes back and forth without any resulting movement
SHM - Simple Harmonic Motion

3. An object in SHM oscillates about a fixed point.
This fixed point is called mean position, or equilibrium position
This is the point where the object would come to rest if no external forces acted on it

4. Describe restoring force
Restoring force, and therefore acceleration, is proportional to the displacement from mean position and directed toward it

5. Examples of SHM: Simple pendulum Mass on a spring Bungee jumping
Diving board
Object bobbing in the water
Earthquakes
Musical instruments

6. Simple Pendululm
Equation:
Time is independent of amplitude or mass

7. Assumptions: 1. Mass of string is negligible compared to mass of load
2. Friction is negligible
3. Angle of swing is small
4. Gravitational acceleration is constant
5. Length is constant

8. Mass on a Spring Time is independent gravitational acceleration
Equation:
Time is independent gravitational acceleration

9. Assumptions: 1. Mass of spring is negligible compared to mass of load
2. Friction is negligible
3. Spring obeys Hooke’s Law at all times
4. Gravitational acceleration is constant
5. Fixed end of spring can’t move

10. Restoring Force is proportional to (-) displacement
Sketch:
Negative sign means force is in the opposite direction of the displacement

11. Variables for SHM: x displacement from mean position
A maximum displacement (amplitude)
Ø phase angle (initial displacement at t = 0)
T period (time for one oscillation)
f frequency (number of oscillations per unit time)
 angular frequency

12. Relationships between variables

13. Other relationships:

14. Diagrams

15. Graphs:

17. Kinetic and Potential Energies in SHM
since

19. Damping
Energy losses (energy dissipation) due to friction - removes energy from system
For an oscillating object with no damping, total energy is constant - depends on mass, square of initial amplitude, angular frequency

20. Damping (continued)
Amplitude decreases exponentially - all energy is eventually converted to heat
Critical damping (controlled)- oscillations die out in shortest time possible

22. Resonance
System displaced from equilibrium position will vibrate at its natural frequency
System can be forced to vibrate with a driving force at the natural frequency
Examples: musical instruments, machinery, glass, microwave, tuning a radio