 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/20/a/solution

ψ_{1}

and

ψ_{2}

solve it, every constant linear combination

A ψ_{1} + B ψ_{2}

The same statement holds for the homogeneous Neumann boundary conditions. Initial conditions combine in the same way; an arbitrary combination need not retain a fixed nonzero initial displacement.

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