Which function represents SHM? (\( \omega \) is a positive constant)
**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) 6 sin (2ω t - (π/4)) : a = -6 (2ω)² sin (2ω t - (π/4)) = -ω² x , SHM. (b) sin ω t + cos 3ω t : Not SHM (mixed frequencies). (c) eω t : Not periodic. (d) cos³ ω t : Periodic, not SHM. Applying x = A cos(ωt +
Ref: NCERT > Physics Book > Oscillations > Damped Oscillations