Please. Answer parts please. Attempt Once. Use cosine and show in rad and degree (2 diff eq) An undamped single-degree-of freedom system consists of a mass 5 kg anda spring of stiffness 2,000 N/m. Find the response of the system when themass is subjected to the following initial conditions:тттт(a) x, = 20 (mm), i = 200(b) x, =-20 (mm), š = 200secsecтmmm(с) х, %3D 20 (тт), х, — — 200(d) х, %3 -20 (тт), х, —- 200secsec 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 -„AsinnIT→ x(t):-cos @,t –@n-sin@,t@nPhase Angle:x(1) = x, cos@,t + 0 sin@,t = Acos(@,t – ø)= tanA,Ø = tantanW,tan otan o := +Wn'n+ X0- Xotan otan oWn= +Wn

Answered: An undamped single-degree-of freedom…

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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Please. Answer parts please. Attempt Once. Use cosine and show in rad and degree (2 diff eq)

An undamped single-degree-of freedom system consists of a mass 5 kg and
a spring of stiffness 2,000 N/m. Find the response of the system when the
mass is subjected to the following initial conditions:
тт
тт
(a) x, = 20 (mm), i = 200
(b) x, =-20 (mm), š = 200
sec
sec
тm
mm
(с) х, %3D 20 (тт), х, — — 200
(d) х, %3 -20 (тт), х, —- 200
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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