The function u = 2sin(\pi x)sin(\pi t/2) describes the vertical displacement at position x and time t,
of a string that is fixed at both ends (x=0 and x=1), and has been plucked, i.e. a vibrating string.
a) Find an expression for the vertical velocity as a function of point along the string.
b) At a fixed time, what point on the string is moving fastest?
c) At a fixed point, when is the string accelerating fastest?