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. Velocity: v = -ω A sin (ω t) , but given v = -8 cos (2t) . ω = 2 s⁻¹, vₘₐₓ = ω A = 8 ⇒ A = (8/2) = 4 m . Since v = -A ω sin (ω t) , adjust phase: x = 4 sin (2t) . Applying x = A cos(ωt + φ), v = -ωA