Choose the correct forms of the Forced Response and the Natural Response of the following system beginning at time t = 0 seconds, y"(t) + 8 y'(t) + 16 y(t) = x(t) if an input signal: x(t) = 2 exp(-4 t) u(t) is applied to the relaxed system. yF(t) = C exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t) = yF(t) C t exp(-4 t) u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(+4 t)u(t) ○ yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(-4 t)u(t) ○ yF(t) = C exp(+4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(+4 t)u(t) OyF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) O yF(t) = C exp(-4 t)u(t); yN(t) = K1 t exp(-4 t) u(t) + K2 t^2 exp(-4 t)u(t) yF(t) = C t^2 exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t) yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
Choose the correct forms of the Forced Response and the Natural Response of the following system beginning at time t = 0 seconds, y"(t) + 8 y'(t) + 16 y(t) = x(t) if an input signal: x(t) = 2 exp(-4 t) u(t) is applied to the relaxed system. yF(t) = C exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t) = yF(t) C t exp(-4 t) u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(+4 t)u(t) ○ yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(-4 t)u(t) ○ yF(t) = C exp(+4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(+4 t)u(t) OyF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) O yF(t) = C exp(-4 t)u(t); yN(t) = K1 t exp(-4 t) u(t) + K2 t^2 exp(-4 t)u(t) yF(t) = C t^2 exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t) yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
Introductory Circuit Analysis (13th Edition)
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I know this question can be solved using laplace transform but, can u help me solve the question (the long way) through diff equations/elementary functions?
![Choose the correct forms of the Forced Response and the Natural Response of the following
system beginning at time t = 0 seconds,
y"(t) + 8 y'(t) + 16 y(t) = x(t)
if an input signal: x(t) = 2 exp(-4 t) u(t) is applied to the relaxed system.
yF(t) = C exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
=
yF(t) C t exp(-4 t) u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(+4 t)u(t)
○ yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(-4 t)u(t)
○ yF(t) = C exp(+4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(+4 t)u(t)
OyF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t)
O yF(t) = C exp(-4 t)u(t); yN(t) = K1 t exp(-4 t) u(t) + K2 t^2 exp(-4 t)u(t)
yF(t) = C t^2 exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F940fea84-314a-4cf2-b65e-4e6cbd95cd4c%2F7f462716-6c0e-46f5-b230-aeb66295a4d6%2F3gkde_processed.png&w=3840&q=75)
Transcribed Image Text:Choose the correct forms of the Forced Response and the Natural Response of the following
system beginning at time t = 0 seconds,
y"(t) + 8 y'(t) + 16 y(t) = x(t)
if an input signal: x(t) = 2 exp(-4 t) u(t) is applied to the relaxed system.
yF(t) = C exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
=
yF(t) C t exp(-4 t) u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(+4 t)u(t)
○ yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 exp(-4 t)u(t)
○ yF(t) = C exp(+4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(+4 t)u(t)
OyF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t)
O yF(t) = C exp(-4 t)u(t); yN(t) = K1 t exp(-4 t) u(t) + K2 t^2 exp(-4 t)u(t)
yF(t) = C t^2 exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
yF(t) = Ct exp(-4 t)u(t); yN(t) = K1 exp(-4 t)u(t) + K2 t exp(-4 t)u(t)
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