Assignment 3.pdf - UBC Mechanical Engineering
Assignment 3.pdf - UBC Mechanical Engineering
Assignment 3.pdf - UBC Mechanical Engineering
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(vii) The functional relation between a through variable and its across variable is called<br />
a. a continuity equation<br />
b. a constitutive equation<br />
c. a compatibility equation<br />
d. a node equation.<br />
(viii) The equation that equates the sum of across variables in a loop to zero is known as<br />
a. a continuity equation<br />
b. a constitutive equation<br />
c. a compatibility equation<br />
d. a ode equation.<br />
(ix) A node equation is also known as<br />
a. an equilibrium equation<br />
b. a continuity equation<br />
c. the balance of through variables at the node<br />
d. all the above.<br />
(x) A loop equation is<br />
a. a balance of across variables<br />
b. a balance of through variables<br />
c. a constitutive relationship<br />
d. all the above.<br />
Problem 2 (Problem 4.2 from Textbook)<br />
A linear graph has 10 branches, two sources, and six nodes.<br />
(i) How many unknown variables are there?<br />
(ii) What is the number of independent loops?<br />
(iii) How many inputs are present in the system?<br />
(iv) How many constitutive equations could be written?<br />
(v) How many independent continuity equations could be written?<br />
(vi) How many independent compatibility equations could be written?<br />
(vii) Do a quick check on your answers.<br />
Problem 3 (Problem 4.3 from Textbook)<br />
The circuit shown in Figure P4.3 has an inductor L, a capacitor C, a resistor R, and a voltage<br />
source v(t). Considering that L is analogous to a spring, and C is analogous to an inertia, follow<br />
the standard steps to obtain the state equations. First sketch the linear graph denoting the currents
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