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  3. a mass weighing 8 lb is attached to a spring hangi

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes...

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Advance Math

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=  

B. What is the resonance frequency for the system?
?0=  

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.

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