A body weighing \(25 \mathrm{lb}\) is suspended from a spring of constant \(k=160\) \(\mathrm{lb} / \mathrm{ft}\). At time \(t=0\), it has a downward velocity of \(2 \mathrm{ft} / \mathrm{sec}\) as it passes through the position of static equilibrium. Determine

(a) the static spring deflection \(\delta_{\text {st }}\)

(b) the natural frequency of the system in both \(\mathrm{rad} / \mathrm{sec}\left(\omega_{n}\right)\) and cycles/sec \(\left(f_{n}\right)\)

(c) the system period \(\tau\)

(d) the displacement \(x\) as a function of time, where \(x\) is measured from the position of static equilibrium

(e) the maximum velocity \(v_{\max }\) attained by the mass

( \(f\) ) the maximum acceleration \(a_{\max }\) attained by the mass.

Transcribed Image Text:

k = 160 lb/ft W = 25 lb