EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Textbook Question
Chapter 9, Problem 4P
Determine the positive roots of the equation
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Consider the homogeneous RLC circuit (no voltage source) shown in the diagram below. Before
the switch is closed, the capacitor has an initial charge go and the circuit has an initial current go.
R
w
i(t)
q(t)
C
н
After the switches closes, current flows through the circuit and the capacitor begins to discharge.
The equation that describes the total voltage in the loop comes from Kirchoff's voltage law:
di(t)
L
+ Ri(t) + (t) = 0,
dt
(1)
where i(t) and q(t) are the current and capacitor charge as a function of time, L is the inductance,
R is the resistance, and C is the capacitance. Using the fact that the current equals the rate of
change of the capacitor charge, and dividing by L, we can write the following homogeneous (no
input source) differential equation for the charge on the capacitor:
ä(t)+2ag(t)+wg(t) = 0,
(2)
where
R
a
2L
and w₁ = C
LC
The solution to this second order linear differential equation can be written as:
where
81=
q(t) = Ae³¹- Bel
82 =
(3)
(4)
(5)
2.
1.
A. Simplify the models in the following block diagrams to open loop models (Y/R = G).
U(s) o
G₁
ROS
G₂
1-GG
G4
X₁
Σ
az
51-
515
G6
G₂
5
G₂
M
b₁
b₂
Σ
o Y(s)
X₁
by
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Chapter 9 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 9 - Prob. 1PCh. 9 - Determine the solution of the equation 3...Ch. 9 - Determine the three roots of the equation...Ch. 9 - Determine the positive roots of the equation...Ch. 9 - The area Aof a circle segment is given by:...Ch. 9 - The position s of the slider as a function of in...Ch. 9 - The van der Waals equation gives a relationship...Ch. 9 - An estimate of the minimum velocity required for a...Ch. 9 - A series RLC circuit with an AC voltage source is...Ch. 9 - For fluid flow in a pipe, the Colebrook-White (or...
Ch. 9 - Using MATLAB’s built-in function fminbnd,...Ch. 9 - A flat rectangular sheet of metal that is 70 in....Ch. 9 - Using MATLAB’s built-in function fminbnd,...Ch. 9 - A prismatic box with equilateral triangular base...Ch. 9 - An RLC circuit with an alternating voltage source...Ch. 9 - A 108-in.-long beam AB is attached to the wall...Ch. 9 - Use MATLAB to calcute the following integrals: (a)...Ch. 9 - Use MATLAB to calculate the following integrals:...Ch. 9 - The speed of a race car during the first 7 s of a...Ch. 9 - A rubber band is stretched by fixing one end...Ch. 9 - Use numerical integration to approximate the size...Ch. 9 - The electric wire that connects the house to the...Ch. 9 - The flow rate Q (volume of fluid per second) in a...Ch. 9 - Prob. 24PCh. 9 - The variation of gravitational acceleration g with...Ch. 9 - An approximate map of Lake Erie is shown in the...Ch. 9 - To estimate the surface area and volume of a...Ch. 9 - Prob. 28PCh. 9 - The orbit of Mercury is elliptical in shape, with...Ch. 9 - Prob. 30PCh. 9 - Use a MATLAB built-in function to numerically...Ch. 9 - Use a MATLAB built-in function to numerically...Ch. 9 - Prob. 33PCh. 9 - Use a MATLAB built-in funtion to numerically...Ch. 9 - The growth of a fish is often modeled by the von...Ch. 9 - A water tank shaped as a cone (R = 2 m, H = 4 m)...Ch. 9 - The sudden outbreak of an insect population can be...Ch. 9 - An airplane uses a parachute and other means of...Ch. 9 - The population growth of species with limited...Ch. 9 - An RL circuit includes a voltage source vs, a...Ch. 9 - Growth of many organisms can be modeled with the...Ch. 9 - The velocity, v, of an object that falls freely...
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