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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, x(0) — —2 sec sec

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, x(0) — —2 sec sec

Elements Of Electromagnetics
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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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
Transcribed Image Text: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
Transcribed Image Text: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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