Question

Suppose a mass weighing 64 lb stretches a spring 2 ft. If the weight is released from rest from 2 ft below the equilibrium position, find the equation of motion x(t) (using Laplace transforms) if an impressed force f(t) = 2 sint acts on the system for 0≤t≤2πand is then removed. Ignore any damping forces.

Answer #1

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
mass is driven by an external force equal to f(t) = 10 cos(3t).
(Use g = 32 ft/s^2 for the acceleration due to...

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
2 ft/sec. Find the equation of motion x(t), provided that the
subsequent motion takes place in a medium that offers a damping
force numerically equal to (1/2) times the instantaneous
velocity

A
mass weighing 3 lb stretches a spring 3 in. If the mass is pushed
upward, contracting the spring a distance of 1 in, and then set in
motion with a downward velocity of 2 ft/s, and if there is no
damping, find the position u of the mass at any time t. Determine
the frequency, period, amplitude, and phase of the motion

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.

Suppose a 64 lb weight stretches a spring 6 inches in
equilibrium and a dashpot provides a damping force of c = 4
lb-sec/ft . Find the displacement of the object if the initial
conditions are:
y(0) = 1.5ft. ,and y 0 (0) = −3ft/sec.
Please show your work step by step, thank you.

A 128 lb weight is attached to a spring whereupon the spring is
stretched 2 ft and allowed to come to rest. The weight is set into
motion from rest by displacing the spring 6 in above its
equilibrium position and also by applying an external force F(t) =
8 sin 4t. Find the subsequent motion of the weight if the
surrounding medium offers a negligible resistance.

A mass weighing 10 lb stretches a spring 1/4 foot. This mass is
removed and replaced with a mass of 1.6 slugs, which is initially
released from a point 1/3 foot above the equilibrium position with
a downward velocity of 3/4 ft/s. Find the first time the mass will
be positioned half of the amplitude below the equilibrium.

A mass weighing 32 lb is attached to a spring hanging from the
ceiling and comes to rest at its equilibrium position. At time t=0,
an external force of F(t) = 3cos(2t) lb is applied to the system.
If the spring constant is 10lb/ft and the damping constant is 4
lb-sec/ft, find the steady state solution for the system. Use g =
32 ft / sec^2

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