chapter 13. oscillations and waves

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