Damping refers to the reduction in oscillation magnitude because of the dissipation of energy. So to take it one step further, damping not only affects the gradual fading of oscillation amplitude, but it also affects the natural frequency of the oscillator.
Damping decreases the natural frequency from its ideal valueand there will be a decrease in the amplitude of the wave.
The highest natural frequency is always decreased by damping, but the lower natural frequencies may either increase or decrease, depending on the form of the damping matrix.
Hence, damping has an effect on the natural frequency of the object.