Oscillations

Linear periodic motion where acceleration

Linear periodic motion where acceleration is directly proportional to displacement from mean position and oppositely directed. Mathematically: a = -ω²

d²x/dt² + ω²x = 0

d²x/dt² + ω²x = 0, derived from F = -kx and Newton's second law. Solution gives x = A sin(ωt + φ), v = Aω cos(ωt + φ), a = -Aω² sin(ωt + φ). The angul

Total energy E = KE +

Total energy E = KE + PE = ½mω²A² remains constant. At mean position: KE = maximum, PE = 0. At extreme positions: KE = 0, PE = maximum. Energy oscilla

Heavy bob suspended by massless string

Heavy bob suspended by massless string performs SHM for small angles (θ < 10°). Period T = 2π√(L/g) is independent of mass and amplitude. Second's pen

Rotational oscillations where restoring torque τ

Rotational oscillations where restoring torque τ = -cθ is proportional to angular displacement. Examples include torsional pendulum and magnet in magn