Question
In: Advanced Math
Consider equation: mx”+cx’+kx=F0cos(\omega t) Find the transient motion and steady periodic oscillations of a damped mass...
Consider equation: mx”+cx’+kx=F0cos(\omega t) Find the transient motion and steady periodic oscillations of a damped mass and spring system with m=1; c=2; and k=26 under the influence of an external force F(t)=82cos(4t) with x(0)=6 and x’(0)=0.
Solutions
Colby Messinger answered 1 year agoRelated Solutions
For a base motion system described by: mx''+ cx'+ kx = cY?b cos ?bt + kY...
For a base motion system described by:
mx''+ cx'+ kx = cY?b cos ?bt + kY sin ?bt
with m = 100 kg, c = 50 N/m, Y = 0.03 m, and ?b = 3 rad/s, find
largest value of the
stiffness k and that makes the transmissibility ratio less than
0.75.
Consider the initial value problem mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest...
Consider the initial value problem
mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0
modeling the motion of a spring-mass-dashpot system initially at
rest and subjected to an applied force F(t), where the unit of
force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms
per second, k=80 Newtons per meter, and F(t)=80cos(8t)
Newtons.
Solve the initial value problem.
x(t)=
Determine the long-term behavior of the system. Is limt→∞x(t)=0? If
it is, enter zero. If not, enter a function that approximates x(t)
for very large positive values...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
determine the steady-state...
An equation of motion is given, where s is in meters and t in seconds. Find...
An equation of motion is given, where s is in meters and t in
seconds. Find (a) the times at which the acceleration is zero, and
(b) the velocity at these times. t^4-10t^3+36t^2+2
*PLEASE SHOW ALL WORK* Consider a damped, forced mass/spring system. Let t denote time (in seconds)...
*PLEASE SHOW ALL WORK*
Consider a damped, forced mass/spring system. Let t denote time
(in seconds) and let x(t) denote the position (in meters) of the
mass at time t, with x = 0 corresponding to the equilibrium
position. Suppose the mass m = 1 kg, the damping constant c = 3
N·s/m, the spring constant k = 2 N/m, the external force is F (t) =
20 cos(2t), the initial position
x(0) = 1 m, and the initial velocity...
Consider the differential equation 2y^2+10y+12 = t+e^t Find the complementary function and particular integral. Hence write...
Consider the differential equation
2y^2+10y+12 = t+e^t
Find the complementary function and particular integral. Hence
write down the full general solution
Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t), with initial condition y(0)=4, A)Find the Laplace transform of the solution...
Consider the differential equation
y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,
A)Find the Laplace transform of the solution
Y(s).Y(s). Write the solution as a single
fraction in s.
Y(s)= ______________
B) Find the partial fraction decomposition of Y(s). Enter all
factors as first order terms in s, that is, all terms
should be of the form (c/(s-p)), where c is a constant and the root
p is a constant. Both c and p may be complex.
Y(s)= ____ + ______ +______
C)...
Consider the following differential equation: (t^2)y'-y=(y^2), where y'=dy/dt. (a) find y(t) if y(1)=1/2 (b)find limt->infinityy(t)
Consider the following differential equation:
(t^2)y'-y=(y^2), where y'=dy/dt.
(a) find y(t) if y(1)=1/2
(b)find limt->infinityy(t)
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