Find the longitudinal vibration response of a uniform bar of length l, fixed at x = 0 and free at x.

Find the longitudinal vibration response of a uniform bar of
length l, fixed at x = 0 and free at x = l, when the end x = 0 is subjected to
an axial harmonic displacement, ub(t) = c sin ωt where c is a constant and
ω is the frequency.

Find the steady state axial motion of a prismatic bar of
length l, fixed at x = 0, when an axial force F (t) = F_{0} acts at the
end x = l using the Laplace transform approach.