### Identify the primary and secondary variables

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1. Construct the weak form of the following linear equation. Identify the primary and secondary variables.

2. Construct the weak form of the following linear equation. Are the boundary conditions "essential" or "natural"?

3. Construct the weak form of the following nonlinear equation. Identify the BC's as either "essential" or "natural."

4. Construct the weak forms of the following nonlinear equations representing the Euler-Bernoulli-von Karman nonlinear theory of beams:

Hint: Look at example 2.4.3 (pg. 502) in the text to see how to find the weak forms for a system of equations.

5. Using a 2-parameter (N = 2) approximation and algebraic polynomials for the basis functions, compute the Ritz coefficients for the approximate solution to

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