Determine the form of the particular solution for the differential equation d v ( t ) d t + 3 v ( t ) = t 2 exp ( − t ) Then, find the particular solution [ Hint: The particular solution includes terms with the same functional forms as the terms found in the forcing function and its derivatives.]
Determine the form of the particular solution for the differential equation d v ( t ) d t + 3 v ( t ) = t 2 exp ( − t ) Then, find the particular solution [ Hint: The particular solution includes terms with the same functional forms as the terms found in the forcing function and its derivatives.]
Solution Summary: The author compares the form of the solution for the given equation and the particular solution.
Determine the form of the particular solution for the differential equation
d
v
(
t
)
d
t
+
3
v
(
t
)
=
t
2
exp
(
−
t
)
Then, find the particular solution [Hint:The particular solution includes terms with the same functional forms as the terms found in the forcing function and its derivatives.]
When the unit step function is applied to the input of the system whose block diagram is given below, the output response takes the value c (0.2) = 0.11 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.
3. (a) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes of this system. (b) Find y(t) the zero-input component of the response for t >= 0, if the initial conditions are y(0) = 1 and y'(0)= -2 for [(D^2)+4D+8]y(t) = Dx(t)
2) In the circuit shown in Fig. 1, the capacitor is initially charged to V0 volts and the switch isclosed at t = 0. Obtain the current, i(t), for t> 0 using the Laplace transform.
Chapter 4 Solutions
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