A beam of length, L, with a uniform cross section and flexural rigidity EI is pinned at its left end and simply supported at its right end. The beam is loaded over its entire length by a uniformly distributed load of intensity w per unit length and at its left end by an externally applied moment, M, as shown in Figure Q2.

Derive expressions for M in terms of w and L that ensure that:- (a) the slope at the left end is zero, (B) the slope at the right end is zero.