Velocity-Displacement Relation in SHM (v = ω√(A² - x²))
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v = ω√(A² - x²)
What each symbol means
| Symbol | What it stands for |
|---|---|
| A | Amplitude (m) |
| v | Speed at displacement x (m/s) |
| x | Displacement from mean position (m) |
| ω | Angular frequency (rad/s) |
When to use this
Gives speed as function of position (not time). Derived from v² = ω²(A² - x²). At x = 0: v = ωA (maximum). At x = ±A: v = 0. Can also be written as v²/ω²A² + x²/A² = 1 (ellipse in phase space). Equivalent to energy conservation: ½mv² + ½kx² = ½kA².