Question
In: Mechanical Engineering
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?
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samet mamat answered 2 years agoRelated Solutions
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 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.
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...
Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c...
Suppose that the mass in a mass-spring-dashpot system with m =
10, the damping constant c = 9, and the spring constant k = 2 is
set in motion with x(0) = -1/2 and x'(0) = -1/4.
(a) Find the position function x(t).
(b) Determine whether the mass passes through its equilibrium
position. Sketch the graph of x(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.
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...
(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 spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity. If the system is driven by
an external force of 9cos(3t)−6sin(3t) N,determine the steady-state
response in the form Rcos(ωt−δ).
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity. If the system is driven by
an external force of 15cos(3t)−10sin(3t) N,determine the
steady-state response in the form Rcos(ωt−δ)
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