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Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]

Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]

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
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Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]
Transcribed Image Text:Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]
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