Practice question

**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°. Velocity: v = -ω A sin (ω t) . ω = 6 s⁻¹, vₘₐₓ = ω A = 12 ⇒ A = (12/6) = 2 m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 2.0 m follows, reflecting SHM dependence on amplitude A, ω and system parameters.