Springs in series and parallel
Simple harmonic motion · Physics
Simple pendulum
Interactive 3DRelease the bob and watch true small-angle SHM. The period depends only on the string length.
Controls
Drag the sliders or type a value — the simulation updates live.
m
0.3m2m
°
5°45°
Study notes
Two springs of k₁ = 100 N/m and k₂ = 300 N/m support a 2-kg mass. Find the oscillation period when they are (a) in series and (b) in parallel. Step 1: (a) Series: 1/k_eq = 1/100 + 1/300 = 4/300 → k_eq = 75 N/m. T = 2π√(2/75) = 2π × 0.1633 ≈ 1.026 s. Step 2: (b) Parallel: k_eq = 100 + 300 = 400 N/m. T = 2π√(2/400) = 2π × 0.0707 ≈ 0.444 s. Answer: (a) ≈ 1.03 s, (b) ≈ 0.44 s. The parallel pair is stiffer, so it oscillates more than twice as fast.