chapter 13. oscillations and waves
TRANSCRIPT
Chapter 11. Oscillations and Waves
11.1. Oscillations and Periodic Motion
Oscillating systems
To oscillate means to move back-and-forth repeatedly. Examples:
• A pendulum [external restoring force]
– A swing
– Rocking chair
– Water waves
• A spring [internal restoring force]
– A guitar string
– Bobble-head doll
– Bond between atoms
Periodic Motion
Any motion that repeats itself over and over at the same time interval is referred to as a periodic motion. Examples:
• A race car on an oval track (perhaps)
• An electrocardiagram
Periodic motion has a repeating cycle. How does it
differ from an oscillation?
An oscillation is symmetric.
Period
Frequency
Hertz
Example 1
Simple Harmonic Motion
Simple Harmonic Motion
Simple Harmonic Motion
If the spring is hung vertically, the only change is in the equilibrium position, which is at the point where the spring force equals the gravitational force.
Simple Harmonic Motion 2
Simple Harmonic Motion 3
Simple Harmonic Motion 4
Simple Harmonic Motion 5
Simple Harmonic Motion 6
Simple Harmonic Motion 7
Its velocity at any position can be computed from conservation of energy:
The Sinusoidal Nature of SHM
The Sinusoidal Nature of SHM
The Sinusoidal Nature of SHM
Simple Harmonic Motion: Summary
Simple Harmonic Motion
If a pen were attached to the mass, it would trace out a sinusoidal wave.
Example 2
Example 2b
Example 3
Example 4
Initial Offset