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...
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
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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...
DIFFERENTIAL EQUATIONS An 8-lb weight is attached to the lower end of a coil spring suspended...
DIFFERENTIAL EQUATIONS
An 8-lb weight is attached to the lower end of a coil spring
suspended from a fixed support. The weight comes to rest in its
equilibrium position, thereby stretching the spring 6 in. The
weight is then pulled down 9 in. below its equilibrium position and
released at t=0. The medium offers a resistance in pounds
numerically equal to 4x', where x' is the instantaneous velocity in
feet per second. Determine the displacement of the weight as a...
Systems of Ordinary Differential Equations
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.
Systems of Ordinary Differential Equations
Let A be a square matrix defined by (a) Find the eigenvalues and eigenspaces of A.(b) Show that A is diagonalizable. Diagonalize A.
A spring is stretched by 7in by a mass weighing 15lb. The mass is attached to...
A spring is stretched by 7in by a mass weighing 15lb. The mass
is attached to a dashpot mechanism that has a damping constant of
0.1lb⋅s/ft and is acted on by an external force of 5cos(9t)lb.
Determine the steady state response of this system. Use 32ft/s2 as
the acceleration due to gravity. Pay close attention to the
units.
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
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