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°. (a) sin ω t + cos ω t : Periodic, period (2π/ω) . (b) sin³ ω t : Periodic, period (2π/3ω) . (c) e⁻ω t : Non-periodic (decays to zero). (d) cos 2ω t : Periodic, period (π/ω) . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result