In: Advanced Math
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.