EBK MATLAB: AN INTRODUCTION WITH APPLIC
5th Edition
ISBN: 8220102007642
Author: GILAT
Publisher: YUZU
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Chapter 11, Problem 9P
The relation between the tension T and the steady shortening velocity v in a muscle is given by the Hill equation:
(T+a)(v+b) = (T0+a)b
where a and b are positive constants and T0is the isometric tension. i.e., the tension in the muscle when v = 0. The maximum shortening velocity occurs when T = 0.
(a) Using symbolic operations, create the Hill equation as a symbolic expression. Then use subs to substitute T = 0, and finally solve for v to show that vmax=bT0)/a. (b) Use vmax from part (a) to eliminate the constant b from the Hill equation, and show that
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c)
An RC circuit is given in Figure Q1.1, where Vi(t) and Vo(t) are the input and
output voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change of Vi(t) applied to the circuit, derive the time
response of Vo(t) with this step change.
Vi(t)
C₁
Vo(1)
R₂ C2 C3 |
R = 20 ΚΩ = 50 ΚΩ
C=C2=C3=25 μF
Figure Q1.1. RC circuit.
c) An RC circuit is given in Figure Q1. vi(t) and vo (t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change vi(t) applied to the circuit, derive and sketch the
time response of the circuit.
R₁ R2
v₁(t)
R3 C₁
v₁(t)
R₁ = R₂ = 10 k
R3
= 100 kn C₁ = 100 μF
Figure Q1. RC circuit.
c)
A RC circuit is given in Figure Q1.1. Vi(t) and Vo(t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii)
With a unit step change of Vi(t) applied to the circuit, derive the time
response of the circuit.
C₁ C₂
Vi(t)
Vo(1)
R₁ C₂
R-25 k C=C2=50 µF
Figure Q1.1. RC circuit.
Chapter 11 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 11 - Prob. 1PCh. 11 - Define y as a symbolic variable and create the two...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Use the commands from Section 11.2 to show that:...Ch. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - The relation between the tension T and the steady...Ch. 11 - Consider the two ellipses in the x y plane given...
Ch. 11 - A 120 in.—long beam AB is attached to the wall...Ch. 11 - A box of mass m is being pulled by a rope as...Ch. 11 - The mechanical power output P in a contracting...Ch. 11 - Prob. 14PCh. 11 - A tracking radar antenna is locked on an airplane...Ch. 11 - Prob. 16PCh. 11 - Define x as a symbolic variable and create the...Ch. 11 - Prob. 18PCh. 11 - The one-dimensional diffusion equation is given...Ch. 11 - A ceramic tile has the design shown in the figure....Ch. 11 - Show that the location of the centroid ycof the...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - The spread of an infection from a single...Ch. 11 - The Maxwell-Boltzmann probability density function...Ch. 11 - The velocity of a skydiver whose parachute is...Ch. 11 - 27. A resistor R (R = 0.4?) and an inductor L (L =...Ch. 11 - Prob. 28PCh. 11 - Determine the solution of the following...Ch. 11 - 30. The current, i, in a series RLC circuit when...Ch. 11 - Damped free vibrations can be modeled by a block...
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