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 distancevalue (x). This system is governed by the following three equations:d²x(t)f₁(t) = mdt²f₂(t) = bdx(t)dtf3 (t) = kxbmF (iv)Suppose that the damping effect of the system is changed (b=10). How will this affect theresponse of the system assuming zero initial conditions? Show all details.(v)Use Laplace transform to find the particular solution of the differential equation from thelast case (when b=10).

Given : To find : Change in response

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 9 f3(t) = kx m k F

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 9 f3(t) = kx m k F

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

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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:
d²x(t)
f₁(t) = m
dt²
f₂(t) = b
dx(t)
dt
f3 (t) = kx
b
m
F

(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).

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