Energy in SHM
In simple harmonic motion, the total mechanical energy remains constant, oscillating between kinetic and potential energy. Total energy E = ½kx_max² = ½mω²A² where k is the spring constant (or effective stiffness), A is amplitude, m is mass, and ω is angular frequency.
Formula
E = ½mω²A²
Real World
A child on a swing has maximum kinetic energy at the lowest point and maximum potential energy at the highest point — total mechanical energy remains constant if we ignore air resistance.
Exam Focus
Show E_k = ½mω²(A² − x²) and E_p = ½mω²x² explicitly; examiners expect both expressions, not just a verbal description of energy exchange.
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