Find the Taylor series for about t 0. Then, assuming that the Laplace transform of can be computed term by term, find an expansion for in powers of .

ME5331 Lecture 9 Consider an object of mass initially at rest on the table. We set the object in motion by a sudden kick at time . Disregarding the friction force, determine the position of the object as a function of time. Such simple occurrence is rather awkward for ordinary mathematics to deal with. From Newton’s second law of motion where we can express the force of the sudden kick on the object by the delta function so that the situation thus described is represented by the IVP We solve this problem applying the Laplace transform. But before we do that, we need to familiarize ourselves with the Laplace transform method applied to linear differential equations with constant coefficients in which the non-homogeneous term is either 0, or a known periodic fu