Practice question

**Effect of damping** is gradual amplitude reduction while period remains nearly constant for light damping. Mechanical energy decreases as work done against damping force, E(t) = ½ k A(t)² decaying exponentially, and motion ceases without external energy input, distinguishing from ideal undamped SHM. SHM requires a = -ω² x : (a) cos ω t + sin 2ω t : Not SHM (mixed frequencies). (b) 4 sin (ω t + (π/6)) : a = -4ω² sin (ω t + (π/6)) = -ω² x , SHM. (c) eω t : Not periodic. (d) sin² ω t : Periodic, not SHM. Applying x = A cos(ωt + φ),