Question

Q-2 Find the transfer function of the system whose differential equation is $ddot{y}(t) + 6 dot{y}(t) + 25 y = 9u(t) + 3dot{u}(t)$ a) Determine the transfer function, $[T(s) = Y(s)/U(s)]$. [10 pts.] b) Take the inverse Laplace transform to determine the impulse response, $y(t)$. [16 pts.] Q-3 Determine the inverse Laplace transform of the following functions: [24 pts.] a) $X(s) =$ [12 pts.] b) $Q(s) =$ [12 pts.] Q-4 Find the Laplace transform of the following time functions: [24 pts.] (a) $y(t) = 1 + 0.6e^{-20t} - 1.6e^{-10t}$ [8 pts.] (b) $f(t) = 3 + 7t + t^2 + delta(t)$ [8 pts.] (c) $f(t) = (t + 1)^2$ [8 pts.]

          Q-2
Find the transfer function of the system whose
differential equation is
$ddot{y}(t) + 6 dot{y}(t) + 25 y = 9u(t) + 3dot{u}(t)$
a) Determine the transfer function, $[T(s) = Y(s)/U(s)]$.
[10 pts.]
b) Take the inverse Laplace transform to determine the
impulse response, $y(t)$.
[16 pts.]
Q-3
Determine the inverse Laplace transform of the
following functions:
[24 pts.]
a) $X(s) =$
[12 pts.]
b) $Q(s) =$
[12 pts.]
Q-4
Find the Laplace transform of the following time
functions:
[24 pts.]
(a) $y(t) = 1 + 0.6e^{-20t} - 1.6e^{-10t}$
[8 pts.]
(b) $f(t) = 3 + 7t + t^2 + delta(t)$
[8 pts.]
(c) $f(t) = (t + 1)^2$
[8 pts.]

Q-2
Find the transfer function of the system whose
differential equation is
ddoty(t) + 6 doty(t) + 25 y = 9u(t) + 3dotu(t)
a) Determine the transfer function, [T(s) = Y(s)/U(s)].
[10 pts.]
b) Take the inverse Laplace transform to determine the
impulse response, y(t).
[16 pts.]
Q-3
Determine the inverse Laplace transform of the
following functions:
[24 pts.]
a) X(s) =
[12 pts.]
b) Q(s) =
[12 pts.]
Q-4
Find the Laplace transform of the following time
functions:
[24 pts.]
(a) y(t) = 1 + 0.6e^-20t - 1.6e^-10t
[8 pts.]
(b) f(t) = 3 + 7t + t^2 + delta(t)
[8 pts.]
(c) f(t) = (t + 1)^2
[8 pts.]

Added by Sara S.

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