Download - Chapter 13. Oscillations and Waves
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Chapter 11. Oscillations and Waves
11.1. Oscillations and Periodic Motion
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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
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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.
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Period
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Frequency
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Hertz
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Example 1
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Simple Harmonic Motion
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Simple Harmonic Motion
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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.
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Simple Harmonic Motion 2
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Simple Harmonic Motion 3
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Simple Harmonic Motion 4
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Simple Harmonic Motion 5
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Simple Harmonic Motion 6
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Simple Harmonic Motion 7
Its velocity at any position can be computed from conservation of energy:
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The Sinusoidal Nature of SHM
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The Sinusoidal Nature of SHM
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The Sinusoidal Nature of SHM
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Simple Harmonic Motion: Summary
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Simple Harmonic Motion
If a pen were attached to the mass, it would trace out a sinusoidal wave.
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Example 2
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Example 2b
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Example 3
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Example 4
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Initial Offset