A mass weighing 8 lb is attached to a springhanging from the ceiling, and comes to rest at its equilibriumposition. The spring constant is 4 lb/ft and thereis no damping.
A. How far (in feet) does the mass stretch the spring from itsnatural length?
L=Â Â
B. What is the resonance frequency for the system?
?0=Â Â
C. At time t=0 seconds, an external forceF(t)=3cos(?0t) is applied to the system(where ?0 is the resonance frequency from part B). Find theequation of motion of the mass.
u(t)=
D. The spring will break if it is extended by 5L feet beyond itsnatural length (where L is the answer in part A). How many timesdoes the mass pass through the equilibrium position travelingdownward before the spring breaks? (Count t=0 as the first suchtime. Remember that the spring is already extended L ft when themass is at equilibrium. Make the simplifying assumption that thelocal maxima of u(t) occur at the maxima of its trigonometricpart.)
times.
