Practice question

**Spring-mass system** has period T = 2π√(m/k), frequency f = (1/2π)√(k/m), ω = √(k/m), where k spring constant (N/m) and m mass (kg). For parallel combination, k_eff = k₁ + k₂, series gives 1/k_eff = 1/k₁ + 1/k₂, affecting ω = √(k_eff/m) and T = 2π√(m/k_eff). T = 2π √((m/k)) . 0.9 = 2π √((0.9/k)) ⇒ (0.9/2π) = √((0.9/k)) . (0.1432)² = (0.9/k) ⇒ k = (0.9/0.0205) ≈ 43.9 N/m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 43.9 N/m follows, reflecting SHM dependence on amplitude A, ω and system parameters.