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

I've attached Handwritten solution for the given problem

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.

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...

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 24 pounds attached to the end of the spring and
stretches it 4 inches. The mass is initially released from rest
from a point 3 inches above the equilibrium position with a
downward velocity of 2 ft/sec.
Find the equation of the motion?

A mass weighing 8 lb is attached to a spring hanging from the
ceiling, and comes to rest at its equilibrium position. The spring
constant is 9 lb/ft and there is no damping.
A. How far (in feet) does the mass stretch the spring from its
natural length? L=________ (do not include units).
B. What is the resonance frequency for the system?
?0= _________(do not include units).
C. At time t=0 seconds, an external force
F(t)=2cos(?0t) is applied to the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 3 minutes ago

asked 13 minutes ago

asked 33 minutes ago

asked 39 minutes ago

asked 52 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago