An airplane, taxiing on a runway, encounters a bump. As a result, the root of the wing is subjected to a displacement that can be expressed as

\[y(t)= \begin{cases}Y\left(t^{2} / t_{0}^{2}\right), & 0 \leq t \leq t_{0} \\ 0, & t>t_{0}\end{cases}\]

Find the response of the mass located at the tip of the wing if the stiffness of the wing is \(k\) (see Fig. 4.51).

Transcribed Image Text:

FIGURE 4.51 Motion of airplane wing. Wing root Wing, k Equivalent mass, m