  Understanding string dynamics yields insights into the intricate dynamic
behaviors of various filamentary thin structures in nature and industry
covering multiple length scales. In this work, we investigate the planar
dynamics of a flexible string where one end is free and the other end is
subject to transverse and longitudinal motions. Under transverse harmonic
motion, we reveal the propagating pulse structure in the stress profile over
the string, and analyze its role in bringing the system into a chaotic state.
For a string where one end is under longitudinal uniform acceleration, we
identify the wiggling transition, derive the analytical wiggling solution from
the string equations, and present the phase diagram.
