Answered: An underdamped shock absorber is to be…

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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Question

An underdamped shock absorber is to be designed for a motor cycle of mass 200 kg(m). When the shock absorber is subjected to an initial vertical velocity due to a road bump, the resulting displacement-time curve is to be as indicated below. Find the necessary stiffness and damping constants of the shock absorber if the damped period of vibration is to be 10 sec(τd) and the amplitude x1is to be reduced to one-tenth in one half cycle. Example is attached

X1.5
td
=
@₁ =
n
Example 2-14: Shock Absorber for a Motorcycle
An underdamped shock absorber is to be designed for a motor cycle of
mass 200 kg (m). When the shock absorber is subjected to an initial vertical
velocity due to a road bump, the resulting displacement-time curve is to be as
indicated below. Find the necessary stiffness and damping constants of
the shock absorber if the damped period of vibration is to be 2 sec (T)
and the amplitude x₁ is to be reduced to one-fourth in one half cycle
X₁
(i.e., X₁.5 ).
4
4
2
2π
@d
X2
=
k/2
700000,
c = 2√√km =
Cc
X1.5X₁
=
4
16
2
m
mm
k/2
x(t)
O
... →8 = ln
→@j=7, @= @√1-5² -
d
X1.5
X₁
X₂
→
=
= ln(16) = 2.7726 =
= π → @n
x2.5
= 2√√(2,358.2652)(200) = 1,373.54
=
k
2
→ k = mw² = (200)(3.4338)² = 2,358.2652
n
m
с
2 = · → c = c = (0.4037)(1,373.54)=554.4981
T
1-(0.4037)²
N
N• sec
m
m
S 8 =
2πζ
√₁-5²
2πζ
2
√1-5²
N • sec
→=0.4037
= 3.4338
rad
sec

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