Question
In: Advanced Math
Mass Springs Systems problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
Mass Springs Systems problem (Differential Equations)
A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches.
If the weight is released from rest at a point 4 inches below the equilibrium position, the system is immersed in a liquid that imparts a damping force numerically equal to 3 times the instantaneous velocity, solve:
a. Deduce the differential equation which models the mass-spring
system.
b. Calculate the displacements of the mass ? (?) at all times
“?”
c. Make a graph that shows the motion
Thanks for the help
Solutions
Colby Messinger answered 1 year agoRelated Solutions
A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from...
A mass weighing 20 pounds stretches a spring 6 inches. The mass
is initially released from rest from a point 8 inches below the
equilibrium position.
(a) Find the position x of the mass at the times
t = π/12, π/8, π/6,
π/4, and 9π/32 s.
(Use
g = 32 ft/s2
for the acceleration due to gravity.)
x(π/12)
=
−14
ft
x(π/8)
=
−.5
ft
x(π/6)
=
−0.25
ft
x(π/4)
=
0.5
ft
x(9π/32)
=
0.35
ft
(b) What is...
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A 4 foot spring measures 8 feet long after a mass
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An 8-lb weight is attached to the lower end of a coil spring
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equilibrium position, thereby stretching the spring 6 in. The
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released at t=0. The medium offers a resistance in pounds
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Let A be a square matrix defined by (a) Find the eigenvalues and eigenspaces of A.(b) Show that A is not diagonalizable but triangularizable. Triangularize A.
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A mass weighing 17 lb stretches a spring 7 in. The mass is attached to a...
A mass weighing 17 lb stretches a spring 7 in. The mass is
attached to a viscous damper with damping constant 2 lb *s/ft. The
mass is pushed upward, contracting the spring a distance of 2 in,
and then set into motion with a downward velocity of 2 in/s.
Determine the position u of the mass at any time t. Use 32 ft/s^2
as the acceleration due to gravity. Pay close attention to the
units. Leave answer in terms of...
A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper...
A mass weighing 12lb stretches a spring 10in.. The mass is
attached to a viscous damper with damping constant 3lb*s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 4in/s.
Determine the position of the mass at any time . Use as 32ft/s^2the
acceleration due to gravity. Pay close attention to the units.
A mass weighing 12lb stretches a spring 10in. The mass is attached to a viscous damper...
A mass weighing 12lb stretches a spring 10in. The mass is
attached to a viscous damper with damping constant 3lb⋅s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 4in/s.
Determine the position u of the mass at any time t. Use 32ft/s2 as
the acceleration due to gravity. Pay close attention to the units.
u(t)=
A mass weighing 19lb stretches a spring 8in. The mass is attached to a viscous damper...
A mass weighing 19lb stretches a spring 8in. The mass is
attached to a viscous damper with damping constant 4lb⋅s/ft. The
mass is pushed upward, contracting the spring a distance of 2in,
and then set into motion with a downward velocity of 7in/s.
Determine the position u of the mass at any time t. Use 32ft/s2 as
the acceleration due to gravity. Pay close attention to the units.
Answer must be in inches
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
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