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

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes to rest at its equilibrium position. The spring constant is 4 lb/ft and there is no damping.

A. How far (in feet) does the mass stretch the spring from its natural length?
L=

B. What is the resonance frequency for the system?
ω0=

C. At time t=0 seconds, an external force F(t)=3cos(ω0t) is applied to the system (where ω0 is the resonance frequency from part B). Find the equation of motion of the mass.
u(t)=

D. The spring will break if it is extended by 5L feet beyond its natural length (where L is the answer in part A). How many times does the mass pass through the equilibrium position traveling downward before the spring breaks? (Count t=0 as the first such time. Remember that the spring is already extended L ft when the mass is at equilibrium. Make the simplifying assumption that the local maxima of u(t) occur at the maxima of its trigonometric part.)
times.

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Expert Solution

Colby Messinger answered 1 year ago

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