A damped harmonic oscillator ẍ(t)+a₁ẋ(t)+a₀x(t)=0 with a₀,a₁>0 is known to be exponentially stable. We extend this result to time-varying positive coefficients a₀(t), a₁(t), t≥0, which are bounded from above and below and satisfy sup_t≥0a₀(t)<(inf_t≥0a₁(t))² and we thus further extend the sufficient condition [Formula presented] by Levin (1969). Under slightly weaker assumptions we show uniform stability.