Question
In: Physics
undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by...
undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by 10 Newtons. Suppose an oscillating force 3 cos(ωt) is acting on the system. What value of ω causes resonance? For this value of ω, find a formula for x, the distance between the weight and equilibrium t seconds after the weight starts at x = 0 at rest.
Solutions
Expert Solution
force by a streched string is
spring constant is
The equation of the spring with force acting on it is
its easy to handle if we use complex equation
and real part of the solution is required
In a steady state, the system oscillates as
inserting into equation
the value of omega that causes resonance is
the formule for x for this value of omega is
where
genius_generous answered 2 years agoRelated Solutions
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 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
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external force of 63cos(12t) lb, determine the position of the mass
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Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 6 meters by a...
Consider a mass-spring-dashpot system with mass 5kg, a spring
which is stretched 6 meters by a force of 20N, and a dashpot which
provides 4N resistance for each m/s of velocity. The mass is also
acted on by a periodic force 5 cos(ωt) for some number ω. For what
value of ω (if any) does practical resonance occur? If the mass
starts at rest, at equilibrium, find a formula for x(t) in terms of
ω, the distance between the mass...
Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 3 meters by a...
Consider a mass-spring-dashpot system with mass 5kg, a spring
which is stretched 3 meters by a force of 10N, and a dashpot which
provides a 4N resistance for each m/s of velocity. The mass is also
acted on by a periodic force 5 cos(ωt) for some number ω.
• For what value of ω (if any) does practical resonance
occur?
• If the mass starts at rest, at equilibrium, find a formula for
x(t) (in terms of ω), the distance...
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 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 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 16 lbin is suddenly set in motion at t=0 by
an external force of 432cos(8t) 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) = ?
A spring with a 6-kg mass and a damping constant 5 can be stretched 1.5 meters...
A spring with a 6-kg mass and a damping constant 5 can be
stretched 1.5 meters beyond its natural length and held at rest
there by a force of 7.5 newtons. Suppose the spring is stretched 3
meters below spring-mass equilibrium and then released with zero
velocity.
Find the position of the mass after t seconds.
y(t)=?
Please show all the work.
A single spring with a 0.75 kg mass on it is stretched out and then released....
A single spring with a 0.75 kg mass on it is stretched out and
then released. Then the velocity of the mass is measured as the
spring passes through its equilibrium position. This experiment is
repeated 18 times; pulling the spring to a different distance each
time. The amplitudes and speeds are listed below.
Amplitude (m.)
Speed at Equilibrium (m/s)
0.05
0.23
0.10
0.38
0.15
0.60
0.20
0.84
0.25
0.98
0.30
1.14
0.35
1.49
0.40
1.63
0.45
1.82
0.50
2.30...
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