Consider a beam $($of Young's modulus E$,$ area of cross$-$section A$,$ moment of inertia I, and length L $)$ with its left end $($ x$=0)$ clamped and its right end $($ x$=$L $)$ supported vertically by a linear elastic spring with spring constant k $.$ The beam has a tip force P applied as shown. Neglect the weight of the beam. Use a single beam finite element

a$.$ Set up the stiffness matrix and force vector for the problem

b$.$ Solve for the tip displacement.

c$.$ Find the reactions at node $1$