A person, carrying a precision instrument of mass \(m\), rides in the elevator of a building in a standing position (Fig. 4.63). The elevator, while moving with velocity \(v_{0}\) at time \(t=0\), decelerates to zero velocity (stops) in time \(\tau\), so that the variation of its velocity can be expressed as

\[u(t)= \begin{cases}u_{0}\left(1-\frac{t}{\tau}\right) ; & 0 \leq t \leq \tau \\ 0 ; & t>\tau\end{cases}\]

Assuming that the stiffness of the person in standing position is \(k\), determine the displacement variation of the precision instrument, \(x(t)\).

Transcribed Image Text:

x(t) m 177 x(t) m y(t) y(t) FIGURE 4.63 Person carrying instrument in elevator.