Period vs Spring Constant
T ∝ 1/√k — stiffer spring → faster.
Key Notes
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.
Formulas
Period vs k
Inverse-square-root in k.
Springs in SERIES
Combined spring softer than either; period LARGER.
Springs in PARALLEL
Combined spring stiffer; period SMALLER.
Ratio at different k
Useful for comparison.
Important Points
Stiffer spring (larger k) ⇒ FASTER oscillation (smaller T).
T ∝ 1/√k — inverse square root.
Series and parallel for springs are OPPOSITE of resistors: series softer (smaller k_eq), parallel stiffer.
Doubling k decreases T by factor √2.
Stiff materials like steel have very high k for their size — used in precision oscillators.
k depends on cross-sectional area, length, material's shear/Young's modulus.
Period vs Spring Constant notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.