{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

332-1solutions

# 332-1solutions - ECE 332 Homework#1 1 Consider the...

This preview shows pages 1–9. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 332 Homework #1 1) Consider the spring—mass system shown below. The input u is force, and the output y is the deﬂection from the equilibrium position. The mass and spring constant are m : k = 1. (A, MW a) Verify that the system is governed by the differential equation W) +21," = gum. (Hint: First write Newton’s 2nd law for each mass.) b) Find the eigenvalues of the system. c) Write the general form of the natural response of the system. (1) Find the transfer function. e) Find the poles and zeros, f) Are there any hidden modes? 2) For each of the following rational functions, perform polynomial division of denominator into numerator and write the function as a sum of a polynomial and a strictly proper part. 33 ~32+s+1 a) —————s 2 sit—s. —s~1 b) % 52+1 s‘ —s e—s——1 C) 432+§s+1 2 s i4s‘ i6s i4si1 d) —2s+2 3) For each of the following rational functions, use the euclidean algorithm to ﬁnd the GOD of the numerator and denominator and ﬁnd the poles and zeros. a) 33 32—2 s4——4s3+852+83+4 b) 33 ——s2]«_|:2 s5——s4+53+ 532+s+9 4) In MATLAB, type n : 2; hw14 to run the Euclidean algorithm on a pair of randomly chosen polynomials of degree 2. The program returns the greatest common denominator god of the two polynomials along with the amount of time etime required to compute gcd. For comparison, the program also computes the roots of the polynomials (not displayed) and returns the amount of time rtz'me required to do so. Increase the value of n and notice how etime and rtime change. Continue to increase n until computation time becomes intolerable. How long does it take to run the Euclidean algorithm in this case? ECC 332: HQMWm/L. 1H SQ ‘u/“f C 3w“; * 9 #9 k»; 7“ 7 R q/ .4 (I‘M Ajgw-f “I“ 2‘") 9%!!!) If; M: M —( %i\ ‘h F ‘‘‘‘‘‘ 1;"; VI ... J." J. 7(7/ '" igK/“‘ ): LK‘L”7‘//“‘LLM (Lé ,_, (‘5'!2 ’ 7 Li? /_L Akﬁ’ WTLN‘AQ )4: X/+7<2 > 5 (/1 ”f M - ‘ O'f “ z \ (A +817 Q, + C CN’UEFD 6:! WI)’ ”JV: QV‘Q (" ’/ "“‘ffi-Qﬁ“ Cmufujqf’rj D 1 Cf)“ ANN + 2 '* h a mm M23: w ”1,, 7 M S M \G J!” .,. 2’ 5 + I i 3 L42” “f N; ””7 ,...... x 5 ”r“ F L L 3 {WWW “ I); M S+§5 3 "+Hs+ IS‘~+ ~M/‘3 we Q m“ h" JQQM C((ﬂ a) V 2 “f I! M ‘, ...... __:L_;f WM .3; 5‘ m /o .. I ((2 main 2;: (U. “*5“ + 15+ Z. mi Li I I o ~L «~‘L 2,, *1 ’2. é; / 0 l" v 5‘ {LAQH A} Mm (3H) 2 f 9 ‘ m w.) Li I E 5“ p m 1) C95» ( V ”IL x ”r (T 13. a ~ “H D 3" ”3, is’; 8'»: T 242 m, w ( ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 9

332-1solutions - ECE 332 Homework#1 1 Consider the...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online