Question
In: Math
A spring with a 4-kg mass and a damping constant 3 can be held stretched 1...
A spring with a 4-kg mass and a damping constant 3 can be held
stretched 1 meters beyond its natural length by a force of 4
newtons. Suppose the spring is stretched 2 meters beyond its
natural length and then released with zero velocity, In the
notation of the text, what is the value
?2−4??c2−4mk? m2kg2/sec2m2kg2/sec2 Find the position of
the mass, in meters, after t seconds. Your answer should be a
function of the variable t with the general form
?1???cos(??)+?2???sin(??)c1eαtcos(βt)+c2eγtsin(δt)
Solutions
milcah answered 2 years agoRelated Solutions
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 spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A 1 3 -kg mass is attached to a spring with stiffness 4 N/m. The damping...
A 1 3 -kg mass is attached to a spring with stiffness 4 N/m. The
damping constant for the system is 2 N-sec/m. The mass is displaced
1 2m to the left and given an initial velocity of 2 m/s to the
right.
(a) Determine the equation of the motion of mass and express it
in the form A e αt sin(βt + φ) by finding the constants A, α, β and
φ in radians.
(b) Find the time t...
Consider the undamped forced harmonic oscillator with mass 1 kg, damping coefficient 0, spring constant 4,...
Consider the undamped forced harmonic oscillator with mass 1
kg, damping coefficient 0, spring constant 4, and external force
h(t) = 3cos(t). The mass is initially at
rest in the equilibrium position. You must understand that you can
model this as: y’’ = -4y +3cost;
y(0) = 0; y’(0) = 0.
(5pts) Using the method of Laplace transforms, solve this
initial value problem.
Check your solution solves the IVP.
(4pts) Be sure to check that your solution satisfies both the...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A
force of 3.6 N is required to keep the spring stretched 0.3 m
beyond its natural length. The spring is stretched 0.7 m beyond its
natural length and then released. Find the position of the mass at
any time t. (Assume that movement to the right is the
positive x-direction and the spring is attached to a wall
at the left end.) What is x(t)?
A spring with 2 kg mass has damping constant 14 and a force of 6 Newton...
A spring with 2 kg
mass has damping constant 14 and a force of 6 Newton is required to
keep the spring stretched 0.5 meter beyond its natural length. The
spring is stretched 1 meter beyond its natural length and then is
released with zero initial velocity. If an external force of F(t)=
2sin2t is applied to the system, find the position of the mass at
any time t.
(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant...
(10pts) Consider the damped forced harmonic oscillator with
mass 1 kg, damping coefficient 2, spring constant 3, and external
force in the form of an instantaneous hammer strike (Section 6.4)
at time t = 4 seconds. The mass is initially displaced 2
meters in the positive direction and an initial velocity of 1 m/s
is applied. Model this situation with an initial value problem and
solve it using the method of Laplace transforms.
A mass m = 1 kg is attached to a spring with constant k = 4...
A mass m = 1 kg is attached to a spring with constant k = 4 N/m
and a dashpot with variable damping coefficient c. If the mass is
to be pulled 5 m beyond its equilibrium (stretching the spring) and
released with zero velocity, what value of c ensures that the mass
will pass through the equilibrium position and compress the spring
exactly 1 m before reversing direction?
c =
A mass m = 1 kg is suspended from a spring that is stretched 1 cm...
A mass m = 1 kg is suspended from a spring that is stretched 1
cm
under the influence of the weight of this mass. Now a periodic
force is applied
external of F (t) = 200 cos (vt) on the mass, which was initially
in
static balance. Disregarding all friction, get a relationship
for
position of the mass as a function of time, x (t). Also determine
the value of
ω which will cause resonance to occur
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