This paper proves that the conventional time invariant input shaping technique (IST) can eliminate the residual vibrations in linear time
varying (LTV) systems completely when IST parameters are chosen properly. Through quasi-static analysis, the response of a LTV system
to an arbitrary input is derived. Then it is shown that the residual vibration in the LW system cancels the response to the reference input
with time delay if the responses have opposite phase and same amplitude. This work also presents a method to obtain the proper IST
parameters with which an arbitrary reference trajectory can be shaped to produce vibration free motion. This proof is validated by
simulations for a second order system.