Question
In: Physics
A mass weighing 8 lb stretches a spring 1/2 foot. Then mass is initially released from...
A mass weighing 8 lb stretches a spring 1/2 foot. Then mass is initially released from rest at a point 1
foot above the equilibrium.
a) Solve the equation of motion with no damping.
Use the same spring system and initial conditions as in Problem above. The spring system is now placed in
a medium that offers a damping force equal to 2 times the instantaneous velocity.
b) Solve the equation of motion
c) At what time does the mass go downward through the equilibrium for the first time?
Solutions
genius_generous answered 1 year agoRelated Solutions
A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is
initially released from rest from a point 2 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 2
times the instantaneous velocity. Find the equation of motion
(solve the IVP) if the mass is driven by an external force equal to
f(t) = 5 cos(2t).
Graph the solution. What part of the...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is
initially released from a point 1 foot below equilibrium with an
upward velocity of 4 ft/s.
(a) Find the equation of motion
(b) In correct units, what are the amplitude, period, and
frequency of this simple harmonic motion?
(c) What is the velocity of the mass at ? = 3? 16 seconds?
(d) Find the first three times that the velocity is zero,
expressed both in exact...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
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 due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 5 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 due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 2 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 due to...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring
8
3
feet. The mass is initially released from rest from a point 7
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) = 25
cos(3t).
(Use
g = 32 ft/s2
for the acceleration...
A) A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released...
A)
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 4 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 id riven by an external force equal to f(t) = 20 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...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass
is initially released from rest from a point 7 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) = 25 cos 3t. (Use
g = 32 ft/s2 for the...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16
pounds stretches a spring
8
3
feet. The mass is
initially released from rest from a point 5 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 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...
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