Energy in SHM (E = ½kA² = ½mω²A², KE = ½k(A² - x²), PE = ½kx²)
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E = ½kA² = ½mω²A², KE = ½k(A² - x²), PE = ½kx²
What each symbol means
| Symbol | What it stands for |
|---|---|
| A | Amplitude (m) |
| E | Total mechanical energy (J) — constant |
| k | Spring constant (N/m) |
| x | Displacement from mean position (m) |
| KE | Kinetic energy = ½mv² = ½k(A² - x²) (J) |
| PE | Potential energy = ½kx² (J) |
When to use this
Total energy E = KE + PE = ½kA² is constant (energy conservation). At mean position (x=0): KE = max = ½kA², PE = 0. At extremes (x=±A): KE = 0, PE = max = ½kA². KE and PE each have period T/2. Average KE = Average PE = E/2. E ∝ A². NCERT Eqs. 13.15-13.18.