Period vs Spring Constant

For spring-mass SHM: T = 2π·√(m/k). Period INVERSELY proportional to √k.

Stiffer spring (larger k) ⇒ smaller T (faster oscillation).

Doubling k decreases T by √2 (~0.707×).

T² vs 1/k is linear — slope = 4π²m.

Springs in series: 1/k_eq = 1/k₁ + 1/k₂ ⇒ k_eq SMALLER ⇒ T LARGER (softer combination).

Springs in parallel: k_eq = k₁ + k₂ ⇒ k_eq LARGER ⇒ T SMALLER (stiffer combination).

k is a property of the spring's material and geometry — not amplitude or mass.

Used in tuning forks, watches, accelerometers — selecting k tunes the natural frequency.