Baranov formula in frequency domain for transient lateral vibrating piles is derived by the Fourier transform. Expressions of Winkler parameters k and c are derived by the Baranov formula. Because the rigorous expressions are complicated
they are not suitable for calculating transient lateral vibration of piles
and for this reason the simplified expressions of k and c are derived by asymptotic expansion of the Hankel function. Mobility curve and velocity one at pile head
when k and c are calculated by the rigorous expressions
are compared with those calculated by the simplified ones. Good agreement between the two results indicates that the simplified expressions are effective for transient lateral response of piles.