Question
In: Physics
A mass that weighs 32 lb stretches 4/3 ft of a spring. The mass is initially...
A mass that weighs 32 lb stretches 4/3 ft of a spring. The mass
is initially released from rest from a point 1 ft below the equilibrium
position, and the subsequent movement takes place in a medium
that offers a damping force equal to the instantaneous velocity.
Using differential equations find the position of the mass at time t
if an external force equal to f (t) = 10cos (t) is applied to the mass
Solutions
genius_generous answered 2 years agoRelated Solutions
A 16-lb weight stretches a spring 16 ft. The spring-mass system is in a medium with...
A 16-lb weight stretches a spring 16 ft. The spring-mass
system is in a medium with a damping constant of 1.5 lb-sec/ft,
and an external force given by
f (t)= 3+e^-3t (in pounds) is being applied. What is the
solution function describing the position of the mass at any time
of the mass is released from
1ft below the equilibrium position with an initial velocity of 2
ft/sec downward?
A mass weighing 4 pounds stretches a spring 4/3 ft. The entire system is immersed in...
A mass weighing 4 pounds stretches a spring 4/3 ft. The entire
system is immersed in a fluid offering a damping force numerically
equal to the instantaneous velocity. Beginning at t=0, an external
force equal to f(t)=e^-t is impressed on the system. Determine an
initial valued differential equation for the displacement of the
mass from its equilibrium point at time t>0.
A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from...
A
mass weighing 32 pounds stretches a spring 16 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 if the mass
is driven by an external force equal to f(t)=10cos(3t).
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...
(1 point) A mass weighing 4 lb4 lb stretches a spring 6 in.6 in. The mass...
(1 point) A mass
weighing 4 lb4 lb stretches a spring 6 in.6 in.
The mass is displaced 8 in8 in in the downward direction from its
equilibrium position and released with no initial velocity.
Assuming that there is no damping, and that the mass is acted on by
an external force of 5cos(7t)5cos(7t) lb,
solve the initial value problem describing the motion of the
mass.
For this problem, please remember to use English units: ft, lb,
sec.ft, lb, sec....
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 180cos(8t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 9 lb/in is suddenly set in motion at t=0 by
an external force of 99cos(20t) lb, determine the position of the
mass at any time. Assume that g=32 ft/s2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 33cos(20t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
Enclose arguments of functions in parentheses. For example,
sin(2x).
u(t)=?
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 288cos(4t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
Enclose arguments of functions in parentheses. For example,
sin(2x).
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 4 lbin is suddenly set in motion at t=0 by an
external force of 63cos(12t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
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