Answered: The parameter of a single-degree-of-freedom system are given by m=1 kg. c=5 N-sec/m, and k=16 N/m. Find the response of the system for the following initial…

Elements Of Electromagnetics

7th Edition

ISBN: 9780190698614

Author: Sadiku, Matthew N. O.

Publisher: Oxford University Press

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Use cosine. and show in degree and rad

The parameter of a single-degree-of-freedom system are given by m=1 kg,
c=5 N-sec/m, and k=16 N/m. Find the response of the system for the
following initial conditions:
m
m
(a) x(0) = 0.1 m, ¿(0)=2
(b) x(0) — —0.1 т, {(0)—-2
sec
sec

Case of x,=0:
x(t) = Acos(@,t-ø)→ x(t = 0) = x, =0= Acosø →
→ x(t = 0) = x, = -@¸Asin=
„A→ A=
2
→ x(t)= Acos @,t -
„Asin
n
IT
→ x(t):
-cos @,t –
@n
-sin@,t
@n
Phase Angle:
x(1) = x, cos@,t + 0 sin@,t = Acos(@,t – ø)
= tan
A,
Ø = tan
tan
W,
tan o
tan o :
= +
Wn
'n
+ X0
- Xo
tan o
tan o
Wn
= +
Wn

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