EBK MATLAB: AN INTRODUCTION WITH APPLIC
5th Edition
ISBN: 8220102007642
Author: GILAT
Publisher: YUZU
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Chapter 9, Problem 3P
To determine
To write:
A MATLAB code that finds two 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 2cosx0.5x=1...Ch. 9 - 3. Determine the solution of the equation .
Ch. 9 - 4. Determine the solution of the equation .
Ch. 9 - 5. A box of mass m = 25 kg is being pulled by a...Ch. 9 - 6. A scale is made of two springs, as shown in the...Ch. 9 - An estimate of the minimum velocity required for a...Ch. 9 - 8. The diode in the circuit shown is forward...Ch. 9 - 9. Determine the minimum and the maximum of the...Ch. 9 - A paper cup shaped as a frustum of a cone with...
Ch. 9 - 11. Consider again the block that is being pulled...Ch. 9 - 12. Determine the dimensions (radius r and height...Ch. 9 - 13. Consider the ellipse. Determine the sidesa...Ch. 9 - 14. Planck’s radiation law gives the spectral...Ch. 9 - A 108-in.-long beam AB is attached to the wall...Ch. 9 - 16. Use MATLAB to calculate the following...Ch. 9 - 17. Use MATLAB to calculate the following...Ch. 9 - 18. The speedofarace carduring the first seven...Ch. 9 - 19. The shape of the centroid line of the Gateway...Ch. 9 - The flow rate Q (volume of fluid per second) in a...Ch. 9 - 21. The electric field E due to a charged circular...Ch. 9 - Prob. 22PCh. 9 - The variation of gravitational acceleration g with...Ch. 9 - 24. A cross section of a river with measurements...Ch. 9 - Prob. 25PCh. 9 - Prob. 26PCh. 9 - Prob. 27PCh. 9 - Prob. 28PCh. 9 - Prob. 29PCh. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 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 an ellipsoid (a = 1.5 m, b...Ch. 9 - The sudden outbreak of an insect population can be...Ch. 9 - An airplane uses a parachute and other means of...Ch. 9 - Prob. 37PCh. 9 - An RL circuit includes a voltage source vs, a...Ch. 9 - Prob. 39PCh. 9 - The velocity, v, of an object that falls freely...
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