Two identical springs (\( k = 80 \, \text{N/m} \)) are attached to a \( 2 \, \text{kg} \) mass as in Fig. 13.14. What is
**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. Effective kₑff = 2k = 2 × 80 = 160 N/m . T = 2π √((m/kₑff)) = 2π √((2/160)) = 2π √(0.0125) ≈ 0.702 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.702 s follows, reflecting SHM dependence on amplitude A, ω and system parameters.
Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency