Oscillations and SHM
Many systems oscillate, repeating a motion around equilibrium. The ideal model is simple harmonic motion (SHM), which occurs when the restoring force is proportional to displacement.
For a mass on a spring, this is described by Hooke's law: . SHM traces a sinusoid defined by:
| Quantity | Symbol & Definition |
|---|---|
| Amplitude | , maximum displacement |
| Period | , time for one full cycle |
| Frequency | , cycles per second in hertz |
Key rule: The period of SHM does not depend on amplitude. A big swing and small swing take the same time, making pendulums reliable clocks.
Pitfall: Confusing frequency and period. They are reciprocals (). High frequency means a short period.
Waves and Interference
A wave is a traveling disturbance carrying energy without transporting matter. Key wave quantities are wavelength (distance between repeats), frequency , and speed , tied by:
Waves are classified by their direction of oscillation relative to travel:
| Wave Type | Oscillation Direction | Example |
|---|---|---|
| Transverse | Perpendicular to travel | Light, string |
| Longitudinal | Parallel to travel | Sound |
When overlapping waves meet, they interfere: constructive (reinforcing) or destructive (cancelling).
Pitfall: Thinking a wave carries matter along with it. A cork bobs in place; the water itself stays put while energy moves.