Question
In: Advanced Math
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached...
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2^1/2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/a. (Use g =32 ft/s^2 for the acceleration due to gravity.) a) Find the time at which the mass attains its extreme displacement from the equilibrium position. b) What is the position of the mass at this instant? c) The extreme displacement is equal to..
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Solutions
Colby Messinger answered 2 years agoRelated Solutions
A mass weighing 8 pounds stretches a spring 4 feet. The medium through the mass moves...
A mass weighing 8 pounds stretches a spring 4 feet. The medium
through the mass moves offers a damping force numerically equal to
sqrt(2) times the instantaneous velocity. Find the equation of
motion if mass is released from equilibrium position with a
downward velocity of 5 ft/s. Find the time at which the mass
attains its extreme displacement from the equilibrium position.
What is the position of the mass at this instant? The acceleration
of gravity is g = 32...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is
initially released from rest from a point 2 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 2
times the instantaneous velocity. Find the equation of motion
(solve the IVP) if the mass is driven by an external force equal to
f(t) = 5 cos(2t).
Graph the solution. What part of the...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring
8
3
feet. The mass is initially released from rest from a point 7
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) = 25
cos(3t).
(Use
g = 32 ft/s2
for the acceleration...
A) A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released...
A)
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 4 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 id riven by an external force equal to f(t) = 20 cos 3t use
g=32 ft/s^2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass
is initially released from rest from a point 7 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) = 25 cos 3t. (Use
g = 32 ft/s2 for the...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16
pounds stretches a spring
8
3
feet. The mass is
initially released from rest from a point 5 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...
will rate :-) A mass weighing 8 pounds stretches a spring 2 feet. At t=0 the...
will rate :-)
A mass weighing 8 pounds stretches a spring 2 feet. At t=0 the mass
is released from a point 2 feet above the equilibrium position with
a downward velocity of 4 (ft/s), determine the motion of the
mass.
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
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...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 5 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 due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 2 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 due to...
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