Question
In: Physics
A mass weighing 4 pounds stretches a spring 4/3 ft. The entire system is immersed in...
A mass weighing 4 pounds stretches a spring 4/3 ft. The entire system is immersed in a fluid offering a damping force numerically equal to the instantaneous velocity. Beginning at t=0, an external force equal to f(t)=e^-t is impressed on the system. Determine an initial valued differential equation for the displacement of the mass from its equilibrium point at time t>0.
Solutions
genius_generous answered 2 years agoRelated Solutions
A mass weighing 10 pounds stretches a spring 3 inches. This mass is removed and replaces...
A mass weighing 10 pounds stretches a spring 3 inches. This mass
is removed and replaces with a mass weighing 20 pounds, which is
initially released from a point 4 inches above the equilibrium
position with an upward velocity of 54 ft/s. Find the equation of
motion, x(t) .
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 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...
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...
A mass that weighs 32 lb stretches 4/3 ft of a spring. The mass is initially...
A mass that weighs 32 lb stretches 4/3 ft of a spring. The
mass
is initially released from rest from a point 1 ft below the
equilibrium
position, and the subsequent movement takes place in a
medium
that offers a damping force equal to the instantaneous
velocity.
Using differential equations find the position of the mass at time
t
if an external force equal to f (t) = 10cos (t) is applied to the
mass
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