boundary conditions

In Problems 1–5 solve equation (4) subject to the appropriate boundary conditions. The beam is of length L, and w0 is a constant.
1. (a) The beam is embedded at its left end and free at its right end, and w(x) = w0, 0 < x < L.
(b) Use a graphing utility to graph the deflection curve when w0 = 24EI and L = 1.

2. (a) The beam is simply supported at both ends, and w(x) = w0, 0 < x < L.
(b) Use a graphing utility to graph the deflection curve when w0 = 24EI and L = 1.

3. (a) The beam is embedded at its left end and simply supported at its right end, and w(x) = w0, 0 < x < L.
(b) Use a graphing utility to graph the deflection curve when w0 = 48EI and L = 1.

4. (a) The beam is embedded at its left end and simply supported at its right end, and w(x) = w0 sin(px/L), 0 < x < L.
(b) Use a graphing utility to graph the deflection curve when w0 = 2p3EI and L = 1.
(c) Use a root-finding application of a CAS (or a graphic calculator) to approximate the point in the graph in part (b) at which the maximum deflection occurs. What is the maximum deflection?

5. (a) The beam is simply supported at both ends, and w(x) = w0x, 0 < x < L.
(b) Use a graphing utility to graph the deflection curve when w0 = 36EI and L = 1.
(c) Use a root-finding application of a CAS (or a graphic calculator) to approximate the point in the graph in part (b) at which the maximum deflection occurs. What is the maximum deflection?

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