  We study the Cauchy problem for the sine-Gordon equation in the semiclassical
limit with pure-impulse initial data of sufficient strength to generate both
high-frequency rotational motion near the peak of the impulse profile and also
high-frequency librational motion in the tails. We show that for small times
independent of the semiclassical scaling parameter, both types of motion are
accurately described by explicit formulae involving elliptic functions. These
formulae demonstrate consistency with predictions of Whitham's formal
modulation theory in both the hyperbolic (modulationally stable) and elliptic
(modulationally unstable) cases.
