Discussion
Duhamel's integral gives the response of a linear system to
Answer: D
Correct answer: an arbitrary forcing function, by superposing impulse responses
Duhamel's integral treats the load as a succession of infinitesimal impulses, computes the free vibration each would produce, and sums them:
\[ u(t) = \frac{1}{m\omega_d}\int_0^t p(\tau)e^{-\xi\omega_n(t-\tau)}\sin\omega_d(t-\tau)\,d\tau \]
Because it is built on superposition it requires linearity, but it places no restriction on the shape of the load. Harmonic, step, blast and earthquake loading are all covered by the same expression.
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