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An undamped single-degree-of-freedom system has a mass of 1 kg (m) and a stiffness of 2,500 N/m (k). Find the magnitude and the phase of the response of the system when the initial displacement is -2 mm ( x6) and the initial velocity of 100 mm/sec ().

An undamped single-degree-of-freedom system has a mass of 1 kg (m) and a stiffness of 2,500 N/m (k). Find the magnitude and the phase of the response of the system when the initial displacement is -2 mm ( x6) and the initial velocity of 100 mm/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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Please. Answer parts please. Attempt Once. Use cosine and show in rads and degree.

An undamped single-degree-of-freedom system has a mass of 1 kg (m) and a stiffness of 2,500 N/m (k). Find the magnitude and the phase of the response of the system when the initial displacement is -2 mm (X) and the initial velocity of 100 mm/sec (x).
Transcribed Image Text:An undamped single-degree-of-freedom system has a mass of 1 kg (m) and a stiffness of 2,500 N/m (k). Find the magnitude and the phase of the response of the system when the initial displacement is -2 mm (X) and the initial velocity of 100 mm/sec (x).
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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