Two identical springs (\( k = 90 \, \text{N/m} \)) are attached to a \( 1.8 \, \text{kg} \) mass as in Fig. 13.14. What
**Mass-spring dynamics** show T depends on mass and stiffness, independent of amplitude for ideal spring. Given T and m, k = 4π² m/T² extracted, and energy E = ½ k A² connects amplitude to total mechanical energy, illustrating isochronism. Effective kₑff = 2k = 2 × 90 = 180 N/m . T = 2π √((m/kₑff)) = 2π √((1.8/180)) = 2π √(0.01) = 2π × 0.1 ≈ 0.628 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.628 s follows, reflecting SHM dependence on amplitude A, ω and system parameters.
Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs