Designing a balance beam with spring supports at the ends. At the left end, a linear spring with a stiffness of k supports the beam. At the right end, both a linear spring k and a torsional spring with a stiffness of kr supports the beam. Find the deflection as a function of z. p(x)=-p cross section Young's Modulus -E 1. State the ODE that govern bending of beams. 2. Calculate the generic solution to this ODE. 3. State the appropriate boundary conditions. 4. Solve for the integration constants. 5. Graph v(z), 0(2), M(r),and V(a), assuming E= 70G Pa, p= 2000N/m, L=20m, w = 1.5m, h=0.25m, k 100e3N/m, kr 100e6 Nm.