Practice question

**Oscillation of mass attached to spring** follows Hooke's law F = -k x, SHM with ω = √(k/m). Effective stiffness for two identical springs in parallel doubles, k_eff = 2k, increasing frequency by √2, while series halves stiffness to k/2, lowering frequency. Energy E = ½ k_eff A². Period T = 2π √((m/k)) . If k' = 3k and m' = 3m , then T' = 2π √((3m/3k)) = 2π √((m/k)) = T , so the period remains unchanged. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It remains unchanged