1. PHYS16 – Lecture 32
Ch. 15 Oscillations

2. Oscillations pre-question
Is a bouncing ball an example of simple harmonic motion?
Yes No

3. Oscillations pre-question
Two kids are swinging on two swings of the same height – one kid is a little chubbier than the other. Neglecting frictional forces, which kid completes a back and forth swing in the fastest time?
A) The chubby kid
B) The skinny kid
C) The kid who pushes off the ground the best
D) Both complete in the same time

4. Outline for Oscillations
Simple Harmonic Motion
Position, Velocity, Acceleration
Force
Energy
Resonance and Damping

5. Oscillations and Periodic Motion
Simple Harmonic Motion
1) About Equil.
2) Periodic
3) Sinusoidal

6. Discussion: Examples of SHM?
Mass on a Spring
Pendulum
Snowboarder in halfpipe
Bungee jumper
Child on swing
Bobble head doll?

7. Simple Harmonic Motion: Position, Velocity, Acceleration

8. Simple Harmonic Motion
Equilibrium Point

9. Discussion: Phase
Your book says that displacement is in terms of cosine and I just said that it is in terms of sine? Who is right?
There is also a phase term (φ) that let’s you set the initial condition.
If the oscillation starts at A it is a sine with a φ=90 degrees or a cosine
with a φ=0 degrees.

10. SHM Position, Velocity, Acceleration

11. Discussion What is the max speed and when does it occur?
Equilibrium Point

12. Example Question
An object undergoes simple harmonic motion. If the amplitude and period are doubled, the object’s max speed is:
Quadrupled
Doubled
Unchanged
Halved
Quartered

13. Simple Harmonic Motion: Restoring Force

14. Restoring Force
Force that always points back to the equilibrium position – Example = spring
k is just a constant – for a spring it is the spring constant

15. Restoring Force – Spring

16. Discussion: Period
A block on a spring has a period of T. What is the period if:
the mass is doubled?
k is quadrupled?
A is doubled?

17. Restoring Force - Pendulum
What is the period of a pendulum?

18. Simple Harmonic Motion: Energy

19. Energy in SHM

20. Main Points - SHM Movement Restoring Force creates oscillation
Energy is dependent on amplitude