A beam simply supported at both ends is subjected to a constant load Po at its centre (x = L/2). The beam's flexural rigidity is El and is made of a material with mass per unit length p. Determine the complete solution, if the beam's initial velocity is zero, but its initial deflection is forced to be half of the static displacement corresponding to Po. (a) Plot the static deflection and over that plot the first mode (b) Plot the static deflection and over that plot the second mode