A uniform horizontal beam of length, L. units, having a simple support at its left end and a fixed support at its right end will be distorted, due to its own weight, into a curve: y=f(x) as shown in the figure. 0 L y=f(x) This curve is called the deflection curve of the beam and it satisfies the differential equation: E-Idy w along with the four boundary conditions: y(0) = 0, y(L) = 0, y" (0) = 0 y' (L) = 0 Problem: Substitute each boundary condition into the appropriate equation: (2), (3) or (4) from page 17.7 of the article: Topic 17: The Deflection Equation of a Uniform Beam and then solve for the coefficients, C. i=1,2,3,4, to verify that the beam's equation is: y= [2x*-3Lx³ + L³x] 4RFI

dv A model for the velocity v at timetof a certain object faling under the influence cf gravity in a viscous medium is given by the equation 1-. From the direction field shown in the figure to the right, skotch the dt 12 solutions with the initial conditions v(0) = 10, 12, and 19. Why is the value v= 12 calied the "terminal velocity"? Choose the correct skelch of the solutions with the initial conditions v(0) = 10, 12, and 19. O A. OB. Oc.

Consider the direction field below for a differential equation. Use the graph to find the equilibrium solutions. Answer (separate by commas):y =

Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $50000 in the account. Each year the account earns 4% interest, and you deposit $5000 into the account. This can be modeled with the differential equation: dy dt y(0) Solve this differential equation for y(t) = y(t) = = 0.04y + 5000 50000