Practice question

**Mass-spring dynamics** show T depends on mass and stiffness, independent of amplitude for ideal spring. Given T and m, k = 4π² m/T² extracted, and energy E = ½ k A² connects amplitude to total mechanical energy, illustrating isochronism. Net force: F = -2kx , so effective kₑff = 2k = 200 N/m . T = 2π √((m/kₑff)) = 2π √((1/200)) ≈ 0.44 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.44 s follows, reflecting SHM dependence on amplitude A, ω and system parameters.