Derive the response of the system of Figure P6.2 and Chapter Problem 6.11 due to a moment

Question:

Derive the response of the system of Figure P6.2 and Chapter Problem 6.11 due to a moment \(M(t)=10 e^{-2 t} \mathrm{~N} \cdot \mathrm{m}\) applied to the bar.

Data From Chapter Problem 6.11:

Determine the natural frequencies of the system of Figure P6.2 if \(m=2 \mathrm{~kg}\), \(L=1 \mathrm{~m}\) and \(k=1000 \mathrm{~N} / \mathrm{m}\).

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