Practice question

**Velocity and acceleration in SHM** follow from differentiation, showing 90° phase lead of v over x and 180° for a over x. At mean position x=0, a=0, v=±ωA maximum; at extremes x=±A, v=0, a=∓ω²A maximum magnitude, illustrating energy conversion. For SHM, acceleration a = -ω² x . Check by differentiating twice: (a) x = sin ω t + cos 2ω t : Not SHM (different frequencies). (b) x = 2 sin (ω t + (π/4)) : v = 2ω cos (ω t + (π/4)), a = -2ω² sin (ω t + (π/4)) = -ω² x . SHM. (c) x = e⁻ω t : Not periodic,