Question

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

Answer #1

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A mass of 3 kg stretches a spring 61.25 cm. Supposing that there
is no damping and that the mass is set in motion from 0.5 m above
its equilibrium position with a downward velocity of 2 m/s,
determine the position of the mass at any time. Find the amplitude,
the frequency, the period and the phase shift of the motion.

A mass weighing 16 pounds stretches a spring 1 feet. It is
initially released from a point 1 foot above the equilibrium
position with an upward velocity of 6 ft/s. Find the equation of
motion. Determine the amplitude, period, and frequency of motion.
(Use g = 32 ft/s2 for the acceleration due to gravity.)

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.

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.

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.

A mass of 50 g stretches a spring 1.568 cm. If the mass is set
in motion from its equilibrium position with a downward velocity of
40 cm/s, and if there is no damping, determine the position u of
the mass at any time t.
Enclose arguments of functions in parentheses. For example,
sin(2x).
Assume g=9.8 ms2. Enter an exact answer.
u(t)=?

A mass of 100 g stretches a spring 1.568 cm. If the mass is set
in motion from its equilibrium position with a downward velocity of
40 cms, and if there is no damping, determine the position u of the
mass at any time t.
Enclose arguments of functions in parentheses. For example,
sin(2x).

A mass of 100 g stretches a spring 5 cm. If the mass is set in
motion from its equilibrium position with a downward velocity of 10
cm/s, and if there is no damping, determine the position u
of the mass at any time t. (Use g = 9.8
m/s2 for the acceleration due to gravity. Let
u(t), measured positive downward, denote the displacement in meters
of the mass from its equilibrium position at time t
seconds.)
u(t) =
When does...

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...

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...

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