Question
In: Mechanical Engineering
A car and the suspension system are a damped spring, mass system, with a natural frequency...
A car and the suspension system are a damped spring, mass system, with a natural frequency 2 Hz and a damping coefficient 0.2. The car drives at speed V over a road with sinusoidal roughness. The roughness wavelength is 20 m, with a amplitude of 50 cm. What speed does the maximum amplitude of vibration occur? What is the corresponding vibration amplitude?
Please do not use an older solution.
Solutions
samet mamat answered 2 years agoRelated Solutions
A spring mass system with a natural frequency fn = 12 Hz is attached to a...
A spring mass system with a natural frequency fn = 12 Hz is
attached to a vibration table. The table is set to vibrate at 16
Hz, 0.5 g maximum acceleration:
a. What is the amplitude of the table's motion in inches?
b. What is the magnification factor M of this undamped
system?
c. What is the maximum displacement of the mass assuming no
dampening?
d. What is the maximum acceleration of the mass assuming the
packaging can be modeled...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2,
and k = 26, under the influence of an external force F(t) = 82
cos(4t).
a) (8 points) Find the position u(t) of the mass at any time t,
if u(0) = 6 and u 0 (0) = 0
. b) (4 points) Find the transient solution uc(t) and the steady
state solution U(t). How would you characterize these two solutions
in terms of their behavior in...
The displacement of an object in a spring-mass system in free damped oscillation is: 2y''+12y'+26y=0 and...
The displacement of an object in a spring-mass system in free
damped oscillation is:
2y''+12y'+26y=0 and has solution: y1 =−5e^(−3t)*cos(2t−0.5π)
if the motion is under-damped.
If we apply an impulse of the form f(t) = αδ(t−τ) then the
differential equation becomes :
2y''+12y'+26y=αδ(t−τ) and has solution y
=−5e^(−3t)cos(2t−0.5π)+αu(t−τ)w(t−τ) where w(t) =
L(^−1)*(1/(2s^2+12s+26))
a. When should the impulse be applied? In other words what is
the value of τ so that y1(τ) =0 . Pick the positive time closest to
t...
The motion of a forced damped spring system is: ?(?) = 2 sin 4? + ?...
The motion of a forced damped spring system is:
?(?) = 2 sin 4? + ? ^-? cos 6?.
A) What is the driving frequency?
B) What is the transient part?
C) What is the steady-periodic part?
Could someone provide explanations as to how to obtain these
solutions as I am lost?
*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...
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 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 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 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 4 lbin is suddenly set in motion at t=0 by an
external force of 63cos(12t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
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