Question
In: Mechanical Engineering
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.
Solutions
samet mamat answered 2 years agoRelated Solutions
A mass-spring-dashpot system is described by my′′ + cy′ + ky = Fo cos ωt, see...
A mass-spring-dashpot system is described by
my′′ + cy′ + ky = Fo cos ωt,
see §3.6 Eq. (17). This second-order differential equation has been
used in simulations, such as this
one at the PhET site:
https://phet.colorado.edu/en/simulation/legacy/resonance.
For m = 2.53kg, c = 0.502N/(m/s), k = 97.2N/m, Fo =
97.2×0.5N = 48.6N,and ω = 2.6, the equation becomes
2.53y′′ + 0.502y′ + 97.2y = 48.6 cos(ωt) .......................
(1)
(a) Given the initial value
y(0) = 2.20, y′(0) = 0,
solve...
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.
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...
Lets say I have a second order ODE: mx''+kx+bx'=kz+bz' ( an EOM where m=3000, b=2000, k=50000,...
Lets say I have a second order ODE:
mx''+kx+bx'=kz+bz' ( an EOM where m=3000,
b=2000, k=50000, and finally z=.01sin(3.5t)).
In Matlab, how would I use the
Matlab command ode23 to solve this ode assuming zero initial
conditions, range :0-20 seconds.
Consider a system of N classical free particles, where the motion of each particle is described...
Consider a system of N classical free particles, where the
motion of each particle is described by Hamiltonian H =
p2/2m, where m is the mass of the particle and p is the
momentum. (All particles are assumed to be identical.)
(1) Calculate the canonical partition function, internal energy
and specific heat of the given system.
(2) Derive the gas state equation.
10) A continuous-time system is described by the following relation, y(t) = (cos 3t) x (t)...
10) A continuous-time system is described by the following
relation, y(t) = (cos 3t) x (t) where y(t) is the output of the
system and x(t) is the input to the system. D
etermine by sufficient explanation whether the system is: a)
Stable, b) Memoryless, c) Causal, d) Time invariant, e) Linear.
An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .
An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .
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