What happens to the frequency of a spring-mass system if the spring constant is quadrupled and the mass is halved?
**SHM representation** using sine or cosine equivalent with phase offset, ω relates to system parameters like mass and stiffness. Understanding ω and φ permits prediction of position at any time and comparison of two SHM via phase difference Δφ = φ₂ - φ₁. Frequency v = (1/2π) √((k/m)) . If k' = 4k and m' = (m/2) , then v' = (1/2π) √((4k/m/2)) = (1/2π) √((8k/m)) = √(8) · v = 2√(2) · v , doubling the original frequency by √(2) . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result
Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency
