3. The vibration of a cable supporting a suspension bridge can be described by the one- dimensional wave equation, \frac{\partial^{2} u}{\partial t^{2}}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}} The problem has the following boundary and initial conditions: • Is the trial solution u(x,t) = g(t)sin(-x) sensible for this problem, discuss10why/why not. (3) \text { Using the trial solution } u(x, t)=g(t) \sin \left(\frac{n \pi}{10} x\right), \text { convert the wave equation } into a single ODE and find its general solution. (6) c) Write the general solution to the PDE and solve for the unknown constants. (6)

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3. The vibration of a cable supporting a suspension bridge can be described by the one- dimensional wave equation, \frac{\partial^{2} u}{\partial t^{2}}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}} The problem has the following boundary and initial conditions: • Is the trial solution u(x,t) = g(t)sin(-x) sensibl