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. Frequency v = (1/2π) √((k/m)) is determined by the ratio of spring constant to mass, reflecting the system’s stiffness and inertia. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Ratio of spring constant to mass follows, reflecting SHM dependence on amplitude A, ω and system parameters.