Question

ĂŶĄůŝƐĞ ĚĞ Ƶŵ ƐŝƐƚĞŵĂ İƐŝĐŽ ŐĞƌĂůŵĞŶƚĞ Ġ ĨĞŝƚĂ͕ ŶŽĚŽŵşŶŝŽĚŽƚĞŵƉŽ͕ƉŽƌĞƋƵĂĕƁĞƐĚŝĨĞƌĞŶĐŝĂŝƐŽƵ͕ ŶŽ ĚŽŵşŶŝŽ ĚĂ ĨƌĞƋƵġŶĐŝĂ ĐŽŵƉůĞǆĂ͕ ƉŽƌ ŵĞŝŽ ĚĂ ƚƌĂŶƐĨŽƌŵĂĚĂĚĞ>ĂƉůĂĐĞ͘hŵƐŝƐƚĞŵĂĠĐŽŶƐŝĚĞƌĂĚŽ ĞƐƚĄǀĞů ƐĞ͕ Ğ ƐŽŵĞŶƚĞ ƐĞ͕ ƚŽĚŽƐ ŽƐ ƉŽůŽƐ ĚĂ ƐƵĂ ĨƵŶĕĆŽ ĚĞ ƚƌĂŶƐĨĞƌġŶĐŝĂ ĞƐƟǀĞƌĞŵ ĐŽŶƟĚŽƐ ŶŽ ƐĞŵŝƉůĂŶŽĞƐƋƵĞƌĚŽĂďĞƌƚŽ͖ĐĂƐŽĐŽŶƚƌĄƌŝŽ͕ŽƐŝƐƚĞŵĂ Ġ ĐŽŶƐŝĚĞƌĂĚŽ ŝŶƐƚĄǀĞů͘ EĞƐƐĂ ĂŶĄůŝƐĞ͕ ŽƐ ƉŽůŽƐ ĚĂ ĨƵŶĕĆŽĚĞƚƌĂŶƐĨĞƌġŶĐŝĂƐĆŽŽƐǀĂůŽƌĞƐĚĂǀĂƌŝĄǀĞůs͕ ƋƵĞĨĂǌĞŵĐŽŵƋƵĞĂĨƵŶĕĆŽƚĞŶĚĂĂŽŝŶĮŶŝƚŽ͕ƐĞŶĚŽ ƋƵĞŽƐĞŵŝƉůĂŶŽĞƐƋƵĞƌĚŽĂďĞƌƚŽĠĐŽŶƐƟƚƵşĚŽƉŽƌ ŶƷŵĞƌŽƐƌĞĂŝƐŶĞŐĂƟǀŽƐŽƵŶƷŵĞƌŽƐĐŽŵƉůĞǆŽƐĐƵũĂ ƉĂƌƚĞ ƌĞĂů Ġ ŶĞŐĂƟǀĂ͘ ŵ ĚĂĚĂ ŵŽĚĞůĂŐĞŵ͕ ĚŽŝƐ ƐŝƐƚĞŵĂƐƌĞƐƵůƚĂƌĂŵĞŵĚƵĂƐĨƵŶĕƁĞƐĚĞƚƌĂŶƐĨĞƌġŶĐŝĂ ŶŽĚŽŵşŶŝŽĚĂƚƌĂŶƐĨŽƌŵĂĚĂĚĞ>ĂƉůĂĐĞ͕ĚĂĚĂƐƉŽƌ͗ 2 F1(s) = s2 + 6s + 8 1 F2(s) = s2 + 2s + 2 F1(s) F2(s) EĞƐƐĂ ƐŝƚƵĂĕĆŽ͕ ĂƐ ĨƵŶĕƁĞƐ e ƌĞƉƌĞƐĞŶƚĂŵ͕ƌĞƐƉĞĐƟǀĂŵĞŶƚĞ͕

Accepted Answer

A) ƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽ
s1 = –2 e s2 = –4ĞƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕͕
ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽs1 = –1 + j e s2 = –1 – j.

Answer

B) ƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽ
s1 = –2 e s2= –4ĞƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞŝŶƐƚĄǀĞů͕͕
ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽs1 = 2 + j e s2 = 2 – j.

Answer

C) ƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽ
s1= –2 e s2 = –2ĞƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕͕
ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽs1 = –1 + j2 e s2 = –1 – j2.

Answer

D) ƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞŝŶƐƚĄǀĞů͕ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽ
s1 = –8 e s2 = –6ĞƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞŝŶƐƚĄǀĞů͕͕
ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽs1 = 1 + j e s2 = 1 – j.

Answer

E) ƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽ
s1= –6 e s2 = –8ĞƵŵƐŝƐƚĞŵĂĚĞĐŽŶƚƌŽůĞĞƐƚĄǀĞů͕͕
ƉŽŝƐƐĞƵƐƉŽůŽƐƐĆŽs1 = –1 + j e s2 = –1 – j.

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