mechanical system is shown in the figure below. This system consists of a damper (b), spring (k) nd mass (m). A force f(t) can be applied on this system in order to move the mass a specific distance alue (x). This system is governed by the following three equations: f₁(t) = m- d²x(t) dt² f₂(t)=b- dx(t) dt fa(t) = kx F m (1) Formulate a differential equation to express the previous system (apply Newton's Second Law) (ii) If m=2, b=1, and k=6, solve this second order differential equation assuming homogeneous case (f(t)=0). (iii) If someone applied a force f(t)= 2 N (starting at t=0) to the previous system, solve this nonhomogeneous second order differential equation.
mechanical system is shown in the figure below. This system consists of a damper (b), spring (k) nd mass (m). A force f(t) can be applied on this system in order to move the mass a specific distance alue (x). This system is governed by the following three equations: f₁(t) = m- d²x(t) dt² f₂(t)=b- dx(t) dt fa(t) = kx F m (1) Formulate a differential equation to express the previous system (apply Newton's Second Law) (ii) If m=2, b=1, and k=6, solve this second order differential equation assuming homogeneous case (f(t)=0). (iii) If someone applied a force f(t)= 2 N (starting at t=0) to the previous system, solve this nonhomogeneous second order differential equation.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Task 1:
A mechanical system is shown in the figure below. This system consists of a damper (b), spring (k)
and mass (m). A force f(t) can be applied on this system in order to move the mass a specific distance
value (x). This system is governed by the following three equations:
fi(t) = m-
d²x(t)
dt²
f₂(t)=b-
dx(t)
dt
F
k
(0)
Formulate a differential equation to express the previous system (apply Newton's Second
Law)
(ii)
If m=2, b=1, and k=6, solve this second order differential equation assuming homogeneous
case (f(t)=0).
(iii)
If someone applied a force f(t)= 2 N (starting at t=0) to the previous system, solve this
nonhomogeneous second order differential equation.
(iv)
Suppose that the damping effect of the system is changed (b=10). How will this affect the
response of the system assuming zero initial conditions? Show all details.
(v)
Use Laplace transform to find the particular solution of the differential equation from the
last case (when b=10).
fa(t) = kx
זון](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b7501c1-2f50-4f44-bb68-e6beadee55e1%2F8ef9f878-e22f-4ca6-902c-c7e9a0df928c%2Ftruyqamo_processed.png&w=3840&q=75)
Transcribed Image Text:Task 1:
A mechanical system is shown in the figure below. This system consists of a damper (b), spring (k)
and mass (m). A force f(t) can be applied on this system in order to move the mass a specific distance
value (x). This system is governed by the following three equations:
fi(t) = m-
d²x(t)
dt²
f₂(t)=b-
dx(t)
dt
F
k
(0)
Formulate a differential equation to express the previous system (apply Newton's Second
Law)
(ii)
If m=2, b=1, and k=6, solve this second order differential equation assuming homogeneous
case (f(t)=0).
(iii)
If someone applied a force f(t)= 2 N (starting at t=0) to the previous system, solve this
nonhomogeneous second order differential equation.
(iv)
Suppose that the damping effect of the system is changed (b=10). How will this affect the
response of the system assuming zero initial conditions? Show all details.
(v)
Use Laplace transform to find the particular solution of the differential equation from the
last case (when b=10).
fa(t) = kx
זון
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