Question

A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.)

Answer #1

A mass weighing 16 pounds stretches a spring
8
3
feet.
The mass is initially released from rest from a point
3 feet
below the equilibrium position, and the subsequent motion takes
place in a medium that offers a damping force that is numerically
equal to
1
2
the
instantaneous velocity. Find the equation of motion
x(t)
if
the mass is driven by an external force equal to
f(t) = 20 cos(3t).
(Use
g =
32 ft/s2
for
the acceleration...

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 3 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1/2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 10 cos(3t).
(Use g = 32 ft/s^2 for the acceleration due to...

A 4-foot spring measures 8 feet long after a mass weighing 8
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2
times the instantaneous velocity. Find the equation of motion if
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downward velocity of 9 ft/s. (Use
g = 32 ft/s2
for the acceleration due to gravity.)
x(t) =
Find the time at which the mass attains its...

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A mass of 1 slug, when attached to a spring, stretches it 2 feet
and then comes to rest in the equilibrium position. Starting at t =
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A force of 64 pounds stretches a spring 4 feet. A mass of 4
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A
mass weighing 8 pounds stretches a spring 2 feet. At t=0 the mass
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A mass weighing 19.6 N stretches a spring 9.8 cm. The
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A mass weighing 16 pounds is attached to a spring and stretches
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(a) What is the initial value problem that models this
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