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. Effective spring constant in parallel: kₑff = k₁ + k₂ = 50 + 50 = 100 N/m . Period: T = 2π √((m/kₑff)) = 2π √((2/100)) = 2π √(0.02) ≈ 0.89 s (using π ≈ 3.14 ). Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.89 s follows, reflecting SHM dependence