A spring system has \( k = 800 \, \text{N/m}, m = 2 \, \text{kg} \). What is the maximum speed if amplitude is \( 5 \, \
**Angular frequency** ω = 2πf = 2π/T characterizes rapidity, independent of amplitude for SHM. Phase constant φ shifts sine/cosine, allowing any initial condition, e.g., x(0)=0 requires φ=0 for sine form. Displacement, velocity, acceleration share ω but differ in phase by 90° and 180°. ω = √((k/m)) = √((800/2)) = 20 rad/s . vₘₐₓ = ω A = 20 × 0.05 = 1.0 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 1.0 m/s follows, reflecting SHM dependence on amplitude A, ω and system parameters.
Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency