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#sinusoidal

2 public questions tagged with this topic.

Damped Oscillations

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

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Damped Oscillations

Which function represents simple harmonic motion? (\( \omega \) 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) 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),

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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