1. Simple Harmonic Motion (SHM)

2. Mass on a Spring Periodic Motion – any repeated motion.
pendulum

3. Mass on a Spring Equilibrium Position F = 0, a = 0, v = max Compressed
Notice: F always points
towards equilibrium (x=0).
This is called a restoring force.
Compressed
F = max, a = max, v = 0
If there were friction, the mass
would slow down and stop. This
is called damping.
Stretched
F = max, a = max, v = 0

4. Hooke’s Law http://phet.colorado.edu/en/simulation/mass-spring-lab
Force is proportional to displacement
SHM occurs whenever the restoring force is proportional to displacement
k = spring constant (N/m) measures the stiffness of the spring
x = displacement from equilibrium (m)
When might we want damped oscillations?

5. 1. 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?

6. 2. Suppose the spring in problem #1 is replaced with a spring that stretches 36cm from its equilibrium position. What is the new spring’s spring constant? Is the spring stiffer or less stiff than the spring in problem #1?

7. Pendulums Amplitude (A) = max displacement from equilibrium
Period (T) = time to complete one cycle of motion (back and forth)
measured in seconds
Frequency (f) = number of cycles per second (Hertz – Hz)

8. Pendulums Period (T) depends on Length of string (L)
Period (T) depends on
Length of string (L)
acceleration due to gravity (g)
Notice: T does not depend on m or A

9. Mass on a Spring Period (T) depends on mass (m) spring constant (k)
Period (T) depends on
mass (m)
spring constant (k)
Notice: T does not depend on A

10. Energy of SHM

11. 9. a) You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and its period is 12 s. How tall is the tower?

12. Wave Motion A wave is the movement of a disturbance through a medium
A medium is the material the wave travels through
- mechanical waves require a medium
- electromagnetic waves do not require a medium

13. Wave Types Pulse Periodic Sine Transverse Longitudinal
Pulse
Periodic
Sine
Transverse
Longitudinal

14. Transverse Wave

15. Longitudinal Wave

16. Waves Energy of a wave is proportional to A2
Wave Speed (v) depends on the medium
Wave Frequency (f) depends on the source
# of crests passing each second

17. Superposition & Interference

18. Superposition & Interference

20. Reflection

21. Interference Pattern

22. Standing Waves

23. Standing Waves

24. Standing Waves
Harmonic Series: