A particle in SHM has \( a = -16 x \) (in SI units). What is its frequency?
**Damped oscillations** occur when resistive forces dissipate energy, amplitude decays exponentially as A(t) = A₀ e^(-b t/2m), b damping coefficient (kg/s), frequency slightly reduced ω' = √(ω₀² - (b/2m)²). Damping arises from friction or viscosity, energy loss per cycle proportional to velocity squared, motion eventually stops. For SHM, a = -ω² x . Given a = -16 x , ω² = 16 ⇒ ω = 4 rad/s . Frequency: v = (ω/2π) = (4/2 × 3.14) ≈ 0.637 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.637 Hz
Ref: NCERT > Physics Book > Oscillations > Damped Oscillations