quiz2 - E13228 Quiz 2 Name 5 ‘Problem#1 Determine whether...

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Unformatted text preview: E13228 Quiz 2 Name: 5 ‘Problem #1 . Determine whether the following system is linear, time-invariant, dynamic, causal and stable (tip for stability test: consider a unit step function as input). I y(t)= Ix(r)dr [Mean {Imia-w'nvafl'ahf, dgnnmvrc.’ cam-«I, man-Sfabla 15' Problem #2 Solve for the following differential equation y" (I) + 31/0) + 2W) = 2250‘) x(t) = 46'3’110‘) m0) = 0,350) #1. - PROBLEM #3 Find the response y(r) for the system described by the following difi‘erential equation. Use the given inifial condifiuns. ' 2le J’"(t) + 3}”(3‘) + 2W) = EXT?) IO) = 48‘3'140‘) I K0) = 0: y'_(0) = l ‘4"!t)+-33’(t)_+25¢t)=o M141 gm)”, arm)?! (:5. flaw 2:91: t - -z j“) = me “(:3 ma): 14% = o a ii“: I' g’m) = -k.~aka =1 “a“! ' -t -z‘t 32m): e -e Swat-wk qt , 3%) f Sy'ct) 1* 230:) = 4 e - M'th gm): gm): '0 «n- ' ‘ - Hp [t’= C9. N'jp'ft) = ace" mitt) = ‘ice- ‘?c~?c+ac=l.¢ «pea ~, -31- 9 he}; 2 e 3,“) = m’ + m + 2e- kvfka'fZiU J, klgz -k.—2k.-6=o ‘ mm, ‘ - ~t — at. 5.11% 22“.! ~¢efl+2e ft = {It 325 ) 1321;) -.2f.'- --3‘t = ‘4£ use -Ize M 56%): Has”) + I!“ (t) “t at ~-3 ...
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