Homework 1

Derive equations by hand on paper (or on a tablet). Solve for transfer functions using Matlab. Upload pictures of your work to Blackboard for credit.

Problem 1

Find $G(s) = V_{o}(s)/V_{i}(s)$ for the circuit shown below using mesh analysis.

Problem 2

Find $G(s) = V_{o}(s)/V_{i}(s)$ for the circuit shown below using nodal analysis.

Problem 3

Find $G(s) = X_{2}(s)/F(s)$ for the translational system shown below.

Problem 4

Find $G(s) = X_{3}(s)/F(s)$ for the translational system shown below.

Problem 5

Find $G(s) = \theta_{1}(s)/T(s)$ for the rotational system shown below.

Problem 6

Find $G(s) = \theta_{1}(s)/T(s)$ for the rotational system shown below.

Problem 7

The dye bromosulfophthalein (BSP) is used to assess liver function. Find $G(s) = M_{4}(s)/M_{o}(s)$ for the compartment model of liver shown below. Assume all $k = 1 s^{-1}$.

Problem 8

Find $G(s) = H_{2}(s)/Q(s)$ for the hydraulic system shown below. Assume all $R$ and $C$ values equal 1.