Question

A 6lb wieght can stretch a spring 6 inches. Suppose the weight is pulled 4 inches past the equilibrium point and released from rest. The initial equation is y(t)=1/3*cos(8t)+0*sin(8t) Suppose that a damping force given in pounds numerically by 1.5 times the instantaneous velocity in feet per second acts on the 6lb weight. Find the position x of the weight as a funtion of time.

Answer #1

A 64 lb weight is attached to a spring causing it to stretch 3
inches and then comes to rest in the equilibrium position. The
damping force is equal to 3 times the instantaneous velocity.
Starting at t = 0 an external force of 3cos(12t) applied to the
system. Find the steady state solution for the system

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A mass weighing 6 pounds, attached to the end of a spring,
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If the weight is released from rest at a point 4 inches below
the equilibrium position, the system is immersed in a liquid that
offers a damping force numerically equal to 3 times the
instantaneous velocity, solve:
a. Deduce the differential equation that models the mass-spring
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MASS SPRING 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, and the entire 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 that models the mass-spring
system.
b. Calculate the displacements of the mass ? (?)...

Determine C1 and C2 of the following damped motion
A 4-lb weight stretches a spring 4 ft. Initially the weight
released from 2ft above equilibrium position with downward velocity
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subsequent motion takes place in a medium that offers a damping
force numerically equal to (1/2) times the instantaneous
velocity

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/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
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2
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the mass is initially released from the equilibrium position with a
downward velocity of 9 ft/s. (Use
g = 32 ft/s2
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x(t) =
Find the time at which the mass attains its...

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
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motion if the mass is initially released from the equilibrium
position with a 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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